A note on the nonabelian tensor square

Advances in Computing the Nonabelian Tensor Square of Polycyclic Groups

The nonabelian tensor square G⊗G of the group G is the group generated by the symbols g ⊗ h, where g, h ∈ G, subject to the relations gg′ ⊗ h = (gg′ ⊗ h)(g ⊗ h) and g ⊗ hh′ = (g ⊗ h)(g ⊗ hh′) for all g, g, h, h′ ∈ G, where gg′ = gg′g−1 is conjugation on the left. Following the work of C. Miller [18], R. K. Dennis in [10] introduced the nonabelian tensor square which is a specialization of the m...

A Note on Tensor Product of Graphs

Let $G$ and $H$ be graphs. The tensor product $Gotimes H$ of $G$ and $H$ has vertex set $V(Gotimes H)=V(G)times V(H)$ and edge set $E(Gotimes H)={(a,b)(c,d)| acin E(G):: and:: bdin E(H)}$. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of $K_n otimes G$.

A Note on Character Square

We study the finite groups with an irreducible character χ satisfying the following hypothesis: χ2 has exactly two distinct irreducible constituents, and one of which is linear, and then obtain a result analogous to the Zhmud’s ([8]).

A Note on Square Totients

A Note on Square Extensions of Bands

The construction of (associative) square extension of an idempotent groupoid (semigroup) was recently introduced by A. W. Marczak and J. PÃlonka. They proved that all square extensions of a variety of idempotent groupoids also form a variety. In this note we explicitely describe the free objects in semigroup varieties obtained from band varieties by means of associative square extensions, which...