On the structure of groups whose exterior or tensor square is a \(p\)-group.

DOI10.1016/j.jalgebra.2011.12.001zbMath1266.20062OpenAlexW2095260015MaRDI QIDQ435953

Mohsen Parvizi, Peyman Niroomand

Publication date: 13 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.12.001

zbMATH Keywords

finitely generated groupsSchur multipliers\(p\)-groupsnonabelian tensor squaresepicenterexterior centernonabelian exterior squares

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Generators, relations, and presentations of groups (20F05) Cohomology of groups (20J06) Homological methods in group theory (20J05) Extensions, wreath products, and other compositions of groups (20E22) Derived series, central series, and generalizations for groups (20F14)

Related Items (5)

Non-abelian tensor square of finite-by-nilpotent groups ⋮ Boundedly finite conjugacy classes of tensors ⋮ Advances on a construction related to the non-abelian tensor square of a group ⋮ Finiteness of homotopy groups related to the non-abelian tensor product ⋮ Finiteness conditions for the non-abelian tensor product of groups

Cites Work

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• Some computations of non-Abelian tensor products of groups
• The non-Abelian tensor product of finite groups is finite
• On the autocommutator subgroup and absolute centre of a group.
• Van Kampen theorems for diagrams of spaces
• On the nilpotency class and solvability length of nonabelian tensor products of groups
• On groups occurring as center factor groups
• The Schur multiplier of a pair of groups
• The exponents of nonabelian tensor products of groups.
• Subgroups generated by small classes in finite groups
• On the capability of groups
• Non-abelian tensor products of solvable groups
• The non-abelian tensor product of polycyclic groups is polycyclic

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