Some Properties of Certain Subgroups of Tensor Squares of p-Groups |
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| Authors: | Mohammad Reza R. Moghaddam Peyman Niroomand |
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| Affiliation: | 1. Department of Mathematics , Mashhad Branch, Islamic Azad University , Mashhad , Iranand Department of Mathematics, Khayyam Higher Education Institute, Mashhad, Iranmrrm5@yahoo.ca;3. School of Mathematics and Computer Science , Damghan University , Damghan , Iran |
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| Abstract: | ![]()
Let G be a finite p-group of order p n and ?(G) be the subgroup of the tensor square of G generated by all symbols x ? x, for all x in G. In the present article, we construct an upper bound for the order of ?(G) and any extra special p-group. It is also shown that ?(G) ? ?(G/G′). Using our result, we obtain the explicit structure of the tensor square of G and π3 SK(G, 1). Finally, the structure of G will be characterized when the bound is attained. |
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| Keywords: | Extra special p-group Non-abelian p-groups Tensor square of groups |
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