COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

82 W. Lindenberg and L. Gerhards
REFERENCES
1. V. FELSCH and J. NEIJB~~SER: Ein Programm zur Berechnung des Untergruppenverbandes
einer endlichen Gruppe. Mitt. d. Rhein. Westf. Inst. f. Znstr. Mathematik,
Bonn, 2 (1963), 39-74.
2. L. GERHARDS and W. LINDENBERG: Ein Verfahren zur Berechnung des vollstandigen
Untergruppenverbandes endlicher Gruppen auf Dualmaschinen. Num. Math. 7
(1965), l-10.
3. W. LINDENEIERG: Uber eine Darstelhmg von Gruppenelementen in digitalen Rechenautomaten.
Num. Math. 4 (1962), 151-153.
4. J. NEUB~~SER: Untersuchungen des Untergruppenverbandes endlicher Gruppen auf
einer programm-gesteuerten elektronischen Dualmaschine. Num. Math. 2 (1960),
280-292.
A programme for the drawing of lattices
K. FERBER and H. JORGENSEN
THE programme A described here was developed by the second author in
1965/66. It was established when a number of lattices of subgroups had to
be drawn for [2], but it was organized in such a way that it is equally efficient
for drawing a diagram representing any finite semi-order for which the
relations of reflexiveness, transitivity, and antisymmetry hold. However,
for this report we shall use the terms occurring with a lattice of subgroups,
such as “subgroup”, “order”, “conjugate”, “class of conjugate subgroups”,
etc.
For the programme A all subgroups of a group G are numbered in a list
Lo: (1) = Uo, vi, . . ., U,, = G in a fixed way. We shall refer to i as the
list-number of Ui. In the diagram to be drawn, the subgroups are represented
by circles or squares containing the list-number of the subgroup in the
numbering mentioned above. If circles (squares) are connected horizontally,
the corresponding subgroups are conjugate, if they are connected vertically,
the lower one is a maximal subgroup of the higher one (see Fig. 1).
FIG. 1
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