Abstract
A group G is said to be capable if it is isomorphic to the central factor group H/Z(H) for some group H. Let G be a nonabelian group of order p 2 q for distinct primes p and q. In this paper, we compute the nonabelian tensor square of the group G. It is also shown that G is capable if and only if either Z(G) = 1 or p < q and \({G^{\rm ab}=\mathbb{Z}_{p}\times\mathbb{Z}_{p}}\) .
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Rashid, S., Sarmin, N.H., Erfanian, A. et al. On the nonabelian tensor square and capability of groups of order p 2 q . Arch. Math. 97, 299–306 (2011). https://doi.org/10.1007/s00013-011-0304-8
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DOI: https://doi.org/10.1007/s00013-011-0304-8