On the nonabelian tensor square and capability of groups of order \(8q\). (English) Zbl 1282.20024
Summary: We determine the nonabelian tensor square \(G\otimes G\) for groups of order \(8q\), where \(q\) is an odd prime. The Schur multiplier of a group of order \(8q\) is used in determining whether a group of this type is capable.
MSC:
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20C25 | Projective representations and multipliers |
| 20J05 | Homological methods in group theory |
| 19C09 | Central extensions and Schur multipliers |
Keywords:
finite groups; groups of order \(8q\); Schur multipliers; nonabelian tensor squares; capable groups; tensor products; exterior squaresSoftware:
GAPReferences:
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