On families of nilpotent subgroups and associated coset posets

DOI10.1007/S40062-022-00315-WOpenAlexW3156062765MaRDI QIDQ2694509

Bernardo Villarreal, Simon Philipp Gritschacher

Publication date: 3 April 2023

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.06869

zbMATH Keywords

nilpotent groupsimplicial complexsimplicial setcolimit of groupscoset poset2-Engel grouphigher generation

Mathematics Subject Classification ID

Nilpotent groups (20F18) Topological methods in group theory (57M07) Simplicial sets and complexes in algebraic topology (55U10) Commutator calculus (20F12) Engel conditions (20F45)

Cites Work

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• Colimits of abelian groups
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• The coset poset and probabilistic zeta function of a finite group
• Generalisations of a classical theorem about nilpotent groups
• Finite p-groups whose proper subgroups are of class ≤ n
• Commuting elements, simplicial spaces and filtrations of classifying spaces
• Higher commutativity and nilpotency in finite groups
• Nilpotent n-tuples in SU(2)
• Third Engel groups and the Macdonald-Neumann conjecture
• Higher generation by subgroups

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