On \(\mathrm\text{ Ш}\)-rigidity of groups of order \(p^6\). (English) Zbl 1310.20025
Summary: Let \(G\) be a group and \(\mathrm{Out}_c(G)\) be the group of its class-preserving outer automorphisms. We compute \(|\mathrm{Out}_c(G)|\) for all the groups \(G\) of order \(p^6\), where \(p\) is an odd prime. As an application, we observe that for most of the \(\mathrm\text{ Ш}\)-rigid groups \(G\) of order \(p^6\), its Bogomolov multiplier \(B_0(G)\) is zero.
MSC:
| 20D45 | Automorphisms of abstract finite groups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20J06 | Cohomology of groups |
Keywords:
finite \(p\)-groups; class-preserving automorphisms; Ш-rigid groups; outer automorphisms; Bogomolov multipliers; Shafarevich-Tate sets; cohomology classesReferences:
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