COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

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398 R. E. Kalman REFERENCES 1. C. HERMITE : Sur le nombre des racines d'une equation algtbrique comprises entre des limites don&es. Oeuvres 1(1900), 397-414. 2. R. E. KALMAN: On the Hermite-Fujiwara theorem in stability theory. Quart. Appl. Math. 23 (1965), 279-282. 3. B. L. VAN DER WAERDEN: Algebra, 7th edition of Modern Algebra (Springer (Heidelberger Taschenbticher No. 12), 1966). 4. R. E. aLMAN: Mathematical description of linear dynamical systems. SIAM J. Control 1 (1963), 152-192. 5. R. E. KALMAN: Lectures on Algebraic System Theory (Springer Lecture Notes in Mathematics, to appear). 6. B. L. Ho and R. E. KALMAN: Effective construction of linear state-variable models from input/output functions. Regelungstechnik 14 (1966), 545-548. 7. R. E. KALMAN: Irreducible realizations and the degree of a rational matrix. SIAM J. Applied Math. 13 (1965). 520-544. 8. R. EKALMAN and T. S. ENGLAR: A user’s manual for the automatic synthesis program (ASP), NASA Contractor Report CR-475, June 1966,526 pp. 9. R. E. KALMAN: On structural properties of linear, constant, multivariable systems. Proc. 3rd IFAC Congress, London, 1966. List of participants THIS list includes all those who were present at the Conference, and also those who were not present but who contributed to the papers in this volume. DR. E. ALTMANN, Rheinisch-Westftilisches Institut fi.ir Instrumentelle Mathetmatik, 53 Bonn, Wegelerstrasse 6, West Germany. PROFESSOR P. B. BENDIX, Mathematics Department, California Institute of Technology, Pasadena, California 91109, U.S.A. MR. C. BROTT, Mathematisches Seminar der Christian-Albrechts-Universitat, Kiel, Neue Universitat, Olshausenstrasse 40-60, West Germany. MR. R. Bti~ow, Mathematisches Seminar der Christian-Albrechts- Universitat, Kiel, Neue Universitat, Olshausenstrasse, 40-60, West Germany. MR. C. M. CAMPBELL, Department of Pure Mathematics, University of St. Andrews, St. Andrews, Fife, Scotland. MR. J. J. CANNON, Department of Pure Mathematics, University of Sydney, Sydney, Australia. DR. R. F. CHURCHHOUSE, Atlas Computer Laboratory, Chilton, Didcot, Berkshire, England. DR. C. R. J. CLAPHAM, Department of Mathematics, Ahmadu Bello University, Zaria, Northern Nigeria, West Africa. DR. A. M. COHEN, Department of Mathematics, Welsh College of Advanced Technology, Cathays Park, Cardiff, Wales. PROFISSOR HARVEY COHN, Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A. DR. J. H. CONWAY, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge, England. DR. B. CORBAS, Department of Pure Mathematics, The University, Reading, England. DR. J. D&ES, Central Research Institute for Physics, Hungarian Academy of Sciences, P.O.B. 49, Budapest 114, Hungary. DR. M. J. DIJNWOODY, Mathematics Department, University of Sussex, Falmer, Brighton, Sussex, England. MR. V. FELSCH, Mathematisches Seminar der Christian-Albrechts-Universitat, Kiel, Neue Universitlt, Olshausenstrasse 40-60, West Germany. MRS. K. FERBER (n&e Espenhain), Mathematisches Seminar der Christian- Albrechts-Universitat, Kiel, Neue Universitat, Olshausenstrasse 40- 60, West Germany. 399
400 List of participants DR. J. J. FLORENTIN, Centre for Computing and Automation, Royal School of Mines Building, Imperial College, London S.W.7, England. PROFESSOR LESLIE Fox, Oxford ‘University Computing Laboratory, 19 Parks Road, Oxford, England. PROFESSOR J. S. FRAME, Department of Mathematics, Michigan State University, East Lansing, Michigan 48823, U.S.A. DR. LEONHARD GERHARDS, Rheinisch-Westfalisches Institut fiir Instrumentelle Mathematik, 53 Bonn, Wegelerstrasse 6, West Germany. DR. C. M. GLENNIE, Home Office Statistical Branch, Tolworth, Surrey, England. MR. M. J. T. GUY, The University Mathematical Laboratory, Corn Exchange Street, Cambridge, England. PROFESSOR MARSHALL HALL, Department of Mathematics, California Institute of Technology, Pasadena, California 91109, U.S.A. PROFESSOR D. G. HIIGMAN, Department of Mathematics, The University of Michigan, 3220 Angel1 Hall, Ann Arbor, Michigan 48104, U.S.A. PROFESSOR G. HIGMAN, F.R.S., Mathematical Institute, University of Oxford, 24/29 St. Giles, Oxford, England. DR. J. W. P. HIRSCHFELD, Mathematics Department, The University of Sussex, Falmer, Brighton, Sussex, England. DR. J. HOWLETT, Atlas Computer Laboratory, Chilton, Didcot, Berkshire, England. DR. D. R. HUGHES, Department of Mathematics, Westfield College, London N.W.3, England. MR. E. J. HUTTON, I.C.T. Limited, Brandon House, 61 Broadway, Bracknell, Berkshire, England. DR. R. E. INGRAM, S.J., University College, Dublin, Eire (died 6 th October 1967). MR. H. J~~RGENSEN, Mathematisches Seminar der Christian-Albrechts- Universitat, Kiel, Neue Universitlt, Olshausenstrasse 40-60, West Germany. PROFESSOR R. E. KALMAN, Stanford Electronics Laboratories, Stanford University, California 94305, U.S.A. DR. A. D. KEEDWELL, Department of Mathematics, University of Surrey, Stag Hill, Guildford, Surrey, England. PROFESSOR R. KEOWN, Department of Mathematics, University of Arkansas, Fayetteville, Arkansas, U.S.A. PROFESSOR D. E. KNUTH, Mathematics Department, California Institute of Technology, Pasadena, California 91109, U.S.A. PROFESSOR E. F. KRAUSE, Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104, U.S.A. DR. A. LEARNER, Department of Mathematics, Queen Mary College, Mile End Road, London E.l, England. List of participants 401 MR. J. LEECH, Dept. of Computing Science, University of Stirling, Stirling, Scotland. DR. SHEN LIN, Room 2C-523, Bell Telephone Laboratories Inc., Murray Hill, New Jersey 07971, U.S.A. DR. W. LINDENBERG, Rheinisch-Westfalisches Institut ftir Instrumentclle Mathematik, 53 Bonn, Wegelerstrasse 6, West Germany. MR. J. K. S. MCKAY, Atlas Computer Laboratory, Chilton, Didcot, Berkshire, England. DR. D. H. MCLAIN, Computing Centre, University College of South Wales and Monmouthshire, Cathays Park, Cardiff, Wales. DR. W. D. MAURER, College of Engineering, University of California, Berkeley, California 94720, U.S.A. PROFESSOR N. S. MENDELSOHN, Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada. PROFESSOR W. 0. J. MOSER, Department of Mathematics, McGill University, Montreal P.Q., Canada. PROFESSOR THEODORE S. MOTZKIN, Department of Mathematics, University of California, Los Angeles, California 90024, U.S.A. PROFESSOR W. D. MUNN, Mathematics Department, University of Stirling, Stirling, Scotland. DR. J. NEUB~SER, Mathematisches Seminar der Christian-Albrechts-Universitat, Kiel, Neue Universitat, Olshausenstrasse 40-60, West Germany. PROFESSOR L. J. PAIGE, Department of Mathematics, University of California, 405 Hilgard Avenue, Los Angeles, California 90024, U.S.A. DR. ROBERT J. PLEMMONS, Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37916, U.S.A. PROFESSOR J. BARKLEY ROSSER, Math. Research Center, U.S. Army, University of Wisconsin, Madison, Wisconsin 53706, U.S.A. CAPTAIN P. G. RUUD, Department of Mathematics, College of Science, Texas A. & M. University, College Station, Texas 77843, U.S.A. MISS JEAN SCOTT, Computer Department, City University, St. John Street, London E.C.l, England. PROFESSOR JOHN L. SELFRIDGE, Mathematics Department, University of Illinois, Urbana, Illinois 61801, U.S.A. PROFESSOR CHARLES C. SIMS, Department of Mathematics, Rutgers, The State University, New Brunswick, New Jersey 08903, U.S.A. DR. N. M. STEPHENS, School of Mathematics and Physics, University of East Anglia, Wilberforce Road, Norwich NOR 77H, England. MR. H. P. F. SWINNERTON-DYER, Department of Pure Mathematics and Mathematical Statistics 16 Mill Lane, Cambridge, England. PROFESSOR T. TAMURA, Department of Mathematics, University of California, Davis, California 95616, U.S.A.
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COMPUTATIONAL PROBLEMS IN ABSTRACT
Page 3 and 4:
vi Contents E. KRAUSE and K. WESTON
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X Preface I am indebted to the auth
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4 J. Neubiiser 2.3.5. Added in proo
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8 J. Neubiiser Investigations of gr
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12 J. Neubiiser For 1 es 4 r, ws is
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16 J. Neubiiser Investigations of g
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Some examples using coset enumerati
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40 C. M. Campbell Some examples usi
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44 N. S. Mendelsohn for example, in
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48 H. Jiirgensen Calculation with e
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60 V. Fe&h and J. Neubiiser 2. The
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64 L. Gerhards and E. Altmann Autom
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68 L. Gerhards and E. Altmann Autom
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72 L. Gerhards and E. Altmann ni E
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76 W. Lindenberg and L. Gerhards Se
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80 W. Lindenberg and L. Gerhards Se
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84 K. Ferber and H. Jiirgensen The
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7 The construction of the character
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92 John McKay defining multiplicati
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96 John McKay Construction of chara
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100 John McKay In the table, c indi
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104 C. Brott and J. Neubiiser irred
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108 C. Brott and J. Neubiiser eleme
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112 J. S. Frame The characters of t
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116 J. S. Frame 3. The decompositio
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TABLE 5. The Z, character block for
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132 R. Biilow and J. Neubiiser Deri
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A search for simple groups of order
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140 Marshall Hall Jr. Simple groups
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148 Marshall Hall Jr. otherwise no
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152 Marshall Hall Jr. easily found
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160 Marshall Hail Jr. This leads to
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164 Marshall Hall Jr. b= (OO)(Ol, 0
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168 Marshall Hall Jr. 11. R. BRAUER
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172 Charles C. Sims THEOREM 2.3. Th
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176 Charles C. Sims has a set of im
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180 Degrc - No. Order t N (-63 Gene
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An algorithm related to the restric
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A module-theoretic computation rela
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192 A. L. Tritter expressed in the
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196 A. L. Tritter a question is mos
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200 John J. Cannon stack. The Cayle
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, I The computation of irreducible
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208 P. G. Ruud and R. Keown product
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212 P. G. Ruud and R. Keown TX wher
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216 P. G. Ruud and R. Keown 4. L. G
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220 N. S. Mendelsohn where it is kn
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224 Robert J. Plemmons such class [
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228 Robert J. Plemmons ! TOTALS Sem
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232 Takayuki Tamura 8” = 0B if an
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236 Takayuki Tamura Case ,Q = {e).
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240 Takayuki Tamura The calculation
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244 Takayuki Tamura We calculate46
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248 Takayuki Tamura Immediately we
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252 Takayuki Tamura Let U be a subs
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256 Takayuki Tamura TABLE 8. AI1 Se
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I The author and R. Dickinson have
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264 Donald E. Knuth and Peter B. Be
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Page 153 and 154: 296 Donald E. Knuth and Peter B. Be
Page 155 and 156: 300 Lowell J. Paige Non-associative
Page 157 and 158: 304 Lowell J. Paige We may lineariz
Page 159 and 160: 308 T(n) U(n) 0) [VI R-4 C. M. Glen
Page 161 and 162: 312 C. M. Glennie where in each cas
Page 163 and 164: 316 A. D. Keedwell of the elements
Page 165 and 166: A projective coqfiguration J. W. P.
Page 167 and 168: The uses of computers in Galois the
Page 169 and 170: 328 W. D. Maurer mod p; for a facto
Page 171 and 172: 332 J. H. Conway Enumeration of kno
Page 173 and 174: J. H. Conway Enumeration of knots a
Page 175 and 176: 340 J. H. Conway -thus our symmetry
Page 177 and 178: 344 J. H. Conway 2 string links to
Page 179 and 180: 348 J. H. Conway 3 and 4 string lin
Page 181 and 182: 352 Non-alternating J. H. Conway L
Page 183 and 184: 356 J. H. Conway Alternating 11 cro
Page 185 and 186: H. F. Trotter Computations in knot
Page 187 and 188: 364 H. F. Trotter to a. Schubert [1
Page 189 and 190: 368 Shen Lin sequence of squares, t
Page 191 and 192: 372 Harvey Cohn We also consider GZ
Page 193 and 194: 376 Harvey Cohn In the case of Fig.
Page 195 and 196: 380 Harvey Cohn always dictated by
Page 197 and 198: 384 Hans Zassenhaus A real root cal
Page 199 and 200: 388 Hans Zassenhaus the elements A,
Page 201 and 202: 392 Hans Zassenhaus It is clear fro
Page 203: 396 R. E. Kalman Invariant factors
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