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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0264-2,
author = {James Beidleman and Hermann Heineken and Jack Schmidt},
title = {On a class of finite solvable groups},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1598-1604},
zbl = {1291.20014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0264-2}
}
James Beidleman; Hermann Heineken; Jack Schmidt. On a class of finite solvable groups. Open Mathematics, Tome 11 (2013) pp. 1598-1604. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0264-2/
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