On a class of finite solvable groups

• Autorzy: James Beidleman , Hermann Heineken , Jack Schmidt
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

S-permutable subgroup; PST-group; Normalizer; X-group

Kategorie tematyczne

• 20D35: Subnormal subgroups
• 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, π -length, ranks

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1598-1604

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

James Beidleman

• University of Kentucky

autor

Hermann Heineken

• Universität Würzburg

autor

Jack Schmidt

• University of Kentucky

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0264-2