6533b851fe1ef96bd12aa272

RESEARCH PRODUCT

On the Frattini subgroup of a finite group

Stefanos AivazidisAdolfo Ballester-bolinches

subject

p-groupNormal subgroupFinite groupClass (set theory)Algebra and Number Theory010102 general mathematicsFrattini subgroupGroup Theory (math.GR)01 natural sciences010101 applied mathematicsCombinatoricsMathematics::Group TheoryLocally finite groupFOS: Mathematics20D25 20D100101 mathematicsMathematics - Group TheoryUniverse (mathematics)Mathematics

description

We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed.

yearjournalcountryeditionlanguage
2016-05-07
10.1016/j.jalgebra.2016.09.010http://arxiv.org/abs/1605.02228