Commutators of elements of coprime orders in finite groups.

DOI10.1515/FORUM-2012-0127zbMath1311.20021arXiv1208.3177OpenAlexW2962853622MaRDI QIDQ487147

P. V. Shumyatskij

Publication date: 19 January 2015

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3177

zbMATH Keywords

finite groupsalternating groupssolubilitycoprime commutatorspowers of commutators

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Simple groups: alternating groups and groups of Lie type (20D06) Commutator calculus (20F12) Subgroups of symmetric groups (20B35)

Related Items (10)

The order of the product of two elements ⋮ Coprime commutators in \(\mathrm{PSL}(2,q)\). ⋮ Coprime commutators and the nonsoluble length of a finite group ⋮ Strong conciseness of coprime commutators in profinite groups ⋮ Orders of products of elements and nilpotency of terms in the lower central series and the derived series ⋮ A sufficient condition for nilpotency of the nilpotent residual of a finite group ⋮ BOUNDING THE ORDER OF THE NILPOTENT RESIDUAL OF A FINITE GROUP ⋮ Commutators and commutator subgroups in profinite groups ⋮ Coprime commutators in finite groups ⋮ COPRIME COMMUTATORS IN THE SUZUKI GROUPS

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