On some subgroups associated with the tensor square of a group

Document Type: Research Paper

Authors

1 Department of Maths,birjand university

2 Department of math, birjand university

3 Islamic Azad University, Neyshabur branch

Abstract

‎In this paper we present some results about subgroup which is‎ ‎generalization of the subgroup $R_{2}^{\otimes}(G)=\{a\in‎ ‎G|[a,g]\otimes g=1_{\otimes},\forall g\in G\}$ of right‎ ‎$2_{\otimes}$-Engel elements of a given group $G$‎. ‎If $p$ is an‎ ‎odd prime‎, ‎then with the help of these results‎, ‎we obtain some‎ ‎results about tensor squares of p-groups satisfying the law‎ ‎$[x,g,y]\otimes g=1_{\otimes}$‎, ‎for all $x‎, ‎g‎, ‎y\in G$‎. ‎In‎ ‎particular p-groups satisfying the law $[x,g,y]\otimes‎ ‎g=1_{\otimes}$ have abelian tensor squares‎. ‎Moreover‎, ‎we can‎ ‎determine tensor squares of two-generator p-groups of class three‎ ‎satisfying the law $[x,g,y]\otimes g=1_{\otimes}$‎.

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