Some structural results on the non-abelian tensor square of groups

2008/10/25 by Russell D. Blyth, Blyth, Russell D., Francesco Fumagalli +3 · 1 citation
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.0810.4620

Abstract

We study the non-abelian tensor square G⊗ G for the class of groups G that are finitely generated modulo their derived subgroup. In particular, we find conditions on G/G' so that G⊗ G is isomorphic to the direct product of ∇(G) and the non-abelian exterior square G\wedge G. For any group G, we characterize the non-abelian exterior square G\wedge G in terms of a presentation of G. Finally, we apply our results to some classes of groups, such as the classes of free soluble and free nilpotent groups of finite rank, and some classes of finite p-groups.

Cited by

• The Non-Abelian Tensor Square of Finite Metacyclic Groups

Related

• The Non-Abelian Tensor Square of Finite Metacyclic Groups
• A note on finiteness conditions for the non-abelian tensor square of groups
• On some series of a group related to the non-abelian tensor square of groups
• Q-tensor square of finitely generated nilpotent groups, q >= 0
• Linearity problem for non-abelian tensor products