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COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

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14 J. Neubiiser Investigations of groups on computers 15<br />

nent 8. Together with K. Weston [Kr. 3,4] he studied a similar process in<br />

Lie rings and applied a programme for it in the study of Burnside groups of<br />

exponent 5. D. W. Walkup [Wa 1] announces that he has used a computer<br />

(in a way not further described) to show that a certain commutator identity<br />

is best possible.<br />

3.5.2. H. J. Bernstein, 0. Moller and E. Strasser Rapaport [Be 3]<br />

describe a programme for finding factorizations of finite groups.<br />

3.5.3. D. A. Smith [Sm 1] gives an algorithm for the determination of a<br />

basis of a finitely generated abelian group.<br />

4. Acknowledgements. The author wishes to express his indebtedness to<br />

Mr. C. Brott, Mr. V. Billow, Mr. V. Felsch and Mr. J. K. S. McKay for<br />

help in compiling and preparing the material for this article and to the<br />

editor of these proceedings who patiently waited for its completion.<br />

REFERENCES<br />

Ai 1. N. N. ~ZENBERG and A. A. LETI~EVSKI!: On computing on “ECM” represen-<br />

Al 1.<br />

tations of wreath-products of finite groups. Kibernetika (Kiev) 1965, no. 3,<br />

63-71; Math. Rev. 35 (1968), 4315.<br />

S. L. ALTMANN and C. J. BRADLEY: A note on the calculation of the matrix elements<br />

of the rotation group. Phil. Trans. Roy. Sot. London (A) 255 (1962/63),<br />

193-198.<br />

Al 2. S. L. ALTMANN and C. J. BRADLEY: On the symmetries of spherical harmonics.<br />

Phil. Trans. Roy. Sot. London (A) 255 (1962/63), 199-215.<br />

Ap 1. K. APPEL, M. HALL JR. and J. THOMPSON: A search for simple groups of odd<br />

order. Notices American Math. Sot. 8 (1961), 364.<br />

Ap 2. K. I. APPEL and E. T. PARKER : On unsolvable groups of degreep = + + 1, p and<br />

q prime. Canad. J. Math. 19 (1967), 583-589.<br />

Ba 1. P. A. BANDLER: M.A. Thesis, Manchester, 1956.<br />

Be 1. C. T. BENSON and N. S. MENDEL~OHN: A calculus for a certain class of word<br />

Be 2.<br />

problems in groups. J. Combinatorial Theory 1(1966), 202-208.<br />

R. BERGER: A computer method for testing for isomorphism between finite<br />

groups. Mimeographed report for applied mathematics 220. Harvard Univ.<br />

(1962).<br />

Be 3. H. J. BERNSTE<strong>IN</strong>, 0. MOLLER and E. STRA~SER RAPAPORT: Machine factorization<br />

Bi 1.<br />

of groups. Mathematical Algorithms 1.3 (1966), 39-51.<br />

R. L. BMNS, N. METROPOLIS, P. R. STEM and M. B. WELLS: Characters of the<br />

symmetric groups of degree 15 and 16. Math. Tables and other Aids to Computation<br />

8 (1954), 212-216.<br />

Br 1. C. BROTT: Ein Programm zur Bestimmung absolut irreduzibler Charaktere und<br />

Darstellungen endlicher Gruppen. Diplomarbeit, Kiel, 1966.<br />

Br 2. C. BROTT and J. NEUB~~SER: A programme for the calculation of characters and<br />

representations of finite groups. These Proceedings, pp. 101-l 10.<br />

Bu 1. W. BURNSIDE: Theory of Groups of Finite Order (Cambridge Univ. Press, 1911).<br />

Bil 1. R. BARLOW and J. NEUB~SER: On some applications of group-theoretical programmes<br />

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pp. 131-135.<br />

Bii. 2. R. Bii~ow: Eine Ableitung der Kristallklassen im R, mit Hilfe gruppentheoretischer<br />

Programme. Diplomarbeit, Kiel, 1967.<br />

a 1. C. M. CAMPBELL: Some examples using coset enumeration. These Proceedings,<br />

pp. 37-41.<br />

a 2. J. M. CAMPBELL and W. J. LAMBERTH: Symbolic and numeric computation in<br />

group theory. Proc. 3rd Austral. Comp. Conf. 293-296, Canberra, May 1966.<br />

Ca 3. J. CANNON: Some combinatorial and symbol manipulation programs in group<br />

theory. These Proceedings, pp. 199-203.<br />

Co 1. S. COI&T: On the machine calculations of characters of the symmetric group.<br />

Comptes Rendus, 12me Congres math. Scand. Lund, 1953 (1954), 18-23.<br />

Co 2. S. COMBT: Notations for partitions. Math. Tables and other Aids to Computation<br />

9 (1955), 143-146.<br />

Co 3. S. CO&T: i)ber die Anwendung von Bin%rmodellen in der Theorie der Charaktere<br />

der symmetrischen Gruppen. Numer. Math. 1(1959), 90-109.<br />

Co 4. S. COMET: Improved methods to calculate the characters of the symmetric<br />

group. Math. Comp. 14 (1960), 104-117.<br />

Co 5. S. CO&T: Character tables for N&20 of the symmetric groups S,. Kept in the<br />

library of Matematikmaskinnlmnden, P.O. Box 6131, Stockholm 6, Sweden.<br />

Co 6. H. S. M. COXETER and W. 0. J. MOSER: Generators and Relations for Discrete<br />

Groups, 2nd ed. (Springer, Berlin, Giittingen, Heidelberg, 1965).<br />

Cu 1. C. W. CXJRTIS and J. REXNER: Representation Theory of Finite Groups and Associative<br />

Algebras (Interscience, New York, 1962).<br />

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9 (1965). 99-122.<br />

De 1. J. ‘DBN&: Bibliography on application of digital computers in abstract algebra.<br />

Mimeographed extract 1967 of: A bibliography on non-numerical applications<br />

of digital computers. Comput. Rev. 9 (1968), 481-508.<br />

Di 1. J. D. DIXON: High speed computation of group characters. Numer. Math. 10<br />

(1967), 446-450.<br />

El 1. H. ELTERMANN: Programmierung des Coxeter-Moser-Verfahrens zur Abz3ihlung<br />

der Restklassen einer Gruppe nach Untergruppen auf Grund von definierenden<br />

Relationen. Mitt. ZUz.- W. Inst. Znstr. Math. Bonn 2 (1963), 105-108.<br />

Fa 1. G. FAST and T. W. JANSSEN: Non-equivalent four-dimensional generalized magnetic<br />

space-time groups. Technical Report. Institute for Theoretical Physics,<br />

University of Nijmegen, 1967.<br />

Fe 1. H. FELL, M. NEWMAN and E. ORDMAN: Tables of genera of groups of linear<br />

fractional transformations. J. Res. Nat. Bur. Standards, Sect. B, 67B (1963),<br />

61-68.<br />

Fe 2. H. FELSCH: Die Behandlung zweier gruppentheoretischer Verfahren auf elektronischen<br />

Rechemnaschinen. Diplomarbeit, Kiel, 1960.<br />

Fe 3. H. FELXH: Programmierung der Restklassenabz&hlung einer Gruppe nach Untergruppen.<br />

Numer. Math. 3 (1961), 250-256.<br />

Fe 4. H. FELSCH, J. NELJB~~SER and R. RUMBERGER: Gewinnung einer Permutationsdarstellung<br />

einer Gruppe aus definierenden Relationen. Mitt. Rh.- W. Inst. Znstr.<br />

.Math. Bonn 2 (1963), 75-104.<br />

Fe 5. V. FELSCH: Ein Programm zur Berechnung des Untergruppenverbandes und der<br />

Automorphismengruppe einer endlichen Gruppe. Diplomarbeit, Kiel, 1963.<br />

Fe 6. V. FELSCH and J. NEUB~SER: Ein Programm zur Berechnung des Untergruppenverbandes<br />

einer endlichen Gruppe. Mitt. Z?h.- W. Inst. Znstr. Math. Bonn 2 (1963),<br />

39-74.<br />

Fe 7. V. FEIXH and J. NEUBBSER: uber ein Programm zur Berechnung der Automorphismengruppe<br />

einer endlichen Gruppe. Numer. Math. 11(1968), 277-292.<br />

Fe 8. V. FELSCH and J. NEUB~~SER: On a programme for the determination of the automorphism<br />

group of a finite group. These Proceedings pp. 59-60

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