# On a class of finite solvable groups

James Beidleman; Hermann Heineken; Jack Schmidt

Open Mathematics (2013)

- Volume: 11, Issue: 9, page 1598-1604
- ISSN: 2391-5455

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topJames Beidleman, Hermann Heineken, and Jack Schmidt. "On a class of finite solvable groups." Open Mathematics 11.9 (2013): 1598-1604. <http://eudml.org/doc/269133>.

@article{JamesBeidleman2013,

abstract = {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.},

author = {James Beidleman, Hermann Heineken, Jack Schmidt},

journal = {Open Mathematics},

keywords = {S-permutable subgroup; PST-group; Normalizer; X-group; permutable subgroups; system normalizers; Sylow subgroups; nilpotent residuals; subgroup closed classes of groups; factor closed classes of groups},

language = {eng},

number = {9},

pages = {1598-1604},

title = {On a class of finite solvable groups},

url = {http://eudml.org/doc/269133},

volume = {11},

year = {2013},

}

TY - JOUR

AU - James Beidleman

AU - Hermann Heineken

AU - Jack Schmidt

TI - On a class of finite solvable groups

JO - Open Mathematics

PY - 2013

VL - 11

IS - 9

SP - 1598

EP - 1604

AB - 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.

LA - eng

KW - S-permutable subgroup; PST-group; Normalizer; X-group; permutable subgroups; system normalizers; Sylow subgroups; nilpotent residuals; subgroup closed classes of groups; factor closed classes of groups

UR - http://eudml.org/doc/269133

ER -

## References

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