The exponents of nonabelian tensor products of groups.

DOI10.1016/j.jpaa.2007.11.003zbMath1187.20050OpenAlexW2030305810MaRDI QIDQ2481817

Primož Moravec

Publication date: 15 April 2008

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2007.11.003

zbMATH Keywords

locally finite groupsexponentsnonabelian tensor squaresnonabelian tensor products

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Nilpotent groups (20F18) Homological methods in group theory (20J05) Extensions, wreath products, and other compositions of groups (20E22)

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Uses Software

• GAP
• Polycyclic

Cites Work

• Some computations of non-Abelian tensor products of groups
• The non-Abelian tensor product of finite groups is finite
• Group extensions, representations, and the Schur multiplicator
• Schur multipliers and power endomorphisms of groups.
• Van Kampen theorems for diagrams of spaces
• On the nilpotency class and solvability length of nonabelian tensor products of groups
• The Schur multiplier of a pair of groups
• On the nilpotent multipliers of a group
• On the nonabelian tensor square of a \(2\)-Engel group
• On adding relations to homotopy groups
• On the relation between upper central quotients and lower central series of a group
• On the exponent semigroups of finite p-groups
• On the Computation of Certain Homotopical Functors
• Groups with exponent six
• Infinite metacyclic groups and their non-abelian tensor squares
• The non-abelian tensor product of groups and related constructions
• Non-abelian tensor products of solvable groups
• On a construction related to the non-abelian tensor square of a group
• The non-abelian tensor product of polycyclic groups is polycyclic
• On power endomorphisms of n-central groups
• Representations of groups as quotient groups. II. Minimal central chains of a group
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