Finite groups can be generated by a \(\pi\)-subgroup and a \(\pi^\prime\)-subgroup

DOI10.1007/S11856-023-2532-6zbMATH Open1545.20027MaRDI QIDQ6584651

Thomas Breuer, Robert Guralnick

Publication date: 8 August 2024

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

generation of finite groupsfree product of profinite groupsintravariant subgroup

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Generators, relations, and presentations of groups (20F05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Limits, profinite groups (20E18)

Cites Work

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• The McKay conjecture is true for the sporadic simple groups
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• Fixed point ratios in actions of finite exceptional groups of Lie type.
• Topological generation of exceptional algebraic groups
• Solvability of groups of odd order
• A correction to the 41-structure of the Monster, a construction of a new maximal subgroup \(L_2(41)\) and a new Moonshine phenomenon.
• Frobenius subgroups of free profinite products
• Maximal abelian subgroups of free profinite groups
• The classification of the finite simple groups

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