Elementary Abelian subgroups in \(p\)-groups with a cyclic derived subgroup.

DOI10.1016/j.jalgebra.2011.03.013zbMath1238.20024OpenAlexW2128982517MaRDI QIDQ655405

David Bornand

Publication date: 4 January 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.03.013

zbMATH Keywords

finite \(p\)-groupssolvable groupshomotopy types of posetsposets of elementary Abelian subgroupssubgroup complexes

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Classification of homotopy type (55P15) Finite nilpotent groups, (p)-groups (20D15) Homotopy groups of wedges, joins, and simple spaces (55Q20)

Related Items

The automorphism group of a class of nilpotent groups with infinite cyclic derived subgroups, Elementary Abelian subgroups in 2-groups whose derived subgroups are Klein 4-groups, Elementary Abelian subgroups in \(p\)-groups with a cyclic derived subgroup., Truncated Quillen complexes of \(p\)-groups, The automorphism group of a finite \(p\)-group with a cyclic Frattini subgroup, Automorphisms of a class of finite \(p\)-groups with a cyclic derived subgroup, Elementary abelian subgroups in some special \(p\)-groups

Cites Work

• Elementary Abelian subgroups in \(p\)-groups with a cyclic derived subgroup.
• Finite solvable groups whose Quillen complex is Cohen-Macaulay.
• Counterexamples to a fiber theorem
• Type d'homotopie des treillis et treillis des sous-groupes d'un groupe fini. (Homotopy type of lattices and lattices of subgroups of a finite groups)
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• On the homotopy type of the Quillen complex of finite soluble groups
• Hypergraph matching complexes and Quillen complexes of symmetric groups.
• The Quillen complex of groups of symplectic type: the characteristic 2 case.
• A sectional characterization of the Dade group
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