2016
DOI: 10.1134/s0081543816090182
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On intersections of abelian and nilpotent subgroups in finite groups. I

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Cited by 6 publications
(7 citation statements)
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“…by [17,Theorem 1]. So we assume that H is not abelian, so, by the proof of [15, Theorem 4], a Sylow r-subgroup of Ĝ is not abelian.…”
Section: Hall Subgroups Of Odd Ordermentioning
confidence: 99%
See 1 more Smart Citation
“…by [17,Theorem 1]. So we assume that H is not abelian, so, by the proof of [15, Theorem 4], a Sylow r-subgroup of Ĝ is not abelian.…”
Section: Hall Subgroups Of Odd Ordermentioning
confidence: 99%
“…It is easy to see that H ∩ H x consists of diagonal matrices, so H ∩ H x is abelian. Therefore, by [17,Theorem 1], there exists y ∈ G such that…”
Section: Hall Subgroups Of Even Ordermentioning
confidence: 99%
“…It give us a description of pairs of subgroups (A, B) with the condition min G (A, B) ̸ = 1 for primary subgroups and sometimes for nilpotent subgroups A and B. For example, in [2,Theorem 1] it is proved that Min G (A, B) F (G) for any pair of abelian subgroups A and B of G, where F (G) is the Fitting subgroup of G (the greatest normal nilpotent subgroup of G).…”
Section: Introductionmentioning
confidence: 99%
“…Denote by P {2,3} the parabolic subgroup which is generated by monomial elements n r2 , n r3 and unipotent subgroup U corresponding positive roots. The subgroup P {2,3} is invariant under graph automorphism τ of order 2, its Levy subgroups L is isomorphic to the Chevalley group B 2 (2). The product L⟨τ ⟩ is isomorphic to the group Aut(A 6 ).…”
Section: Introductionmentioning
confidence: 99%
“…[8] Let A be an abelian subgroup of a finite group G. Then there exists x ∈ G such that A ∩ A x ≤ F (G).…”
mentioning
confidence: 99%