A new GAP group library for irreducible maximal solvable subgroups of prime degree classical groups. (English) Zbl 0995.20028

Detinko, A. S.

J. Math. Sci., New York 108, No. 6, 942-950 (2002) and Zap. Nauchn. Semin. POMI 258, 71-81 (1999).

Summary: These notes are concerned with the problem of creating new group libraries for the group-theory computer system GAP (groups, algorithms, and programming). Our main objective is to develop efficient algorithms that produce a list of maximal solvable subgroups of special linear groups of prime degree over a finite field and to implement it as part of GAP.

MSC:

20G40	Linear algebraic groups over finite fields
20-04	Software, source code, etc. for problems pertaining to group theory
68W30	Symbolic computation and algebraic computation
20E28	Maximal subgroups
20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20E45	Conjugacy classes for groups

Keywords:

GAP; algorithms; maximal solvable subgroups; special linear groups

Software:

GAP