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On a class of finite solvable groups

100%

Beidleman J., Heineken H., Schmidt J.

Open Mathematics

2013

tom 11

nr 9

1598-1604

A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms.

Algorithms for permutability in finite groups

63%

Ballester-Bolinches A., Cosme-Llópez E., Esteban-Romero R.

Open Mathematics

2013

tom 11

nr 11

1914-1922

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

Ograniczanie wyników

2 Open Mathematics

1 Ballester-Bolinches A.

1 Beidleman J.

1 Cosme-Llópez E.

1 Esteban-Romero R.

1 Heineken H.

1 Schmidt J.

2 2013

Wyniki wyszukiwania

On a class of finite solvable groups

Algorithms for permutability in finite groups