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On a class of finite solvable groups

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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.

Ograniczanie wyników

1 Open Mathematics

1 Beidleman J.

1 Heineken H.

1 Schmidt J.

1 2013

Wyniki wyszukiwania

On a class of finite solvable groups