Classification of finite p-groups of characteristic rank one
This article gives a classification statement for certain kinds of groups of prime power order, subject to additional constraints.
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- is either trivial or extraspecial
- is a cyclic group if is an odd prime. For , is either cyclic, or has a cyclic maximal subgroup with the quotient acting on it by multiplication by either or , where . In particular, it has a cyclic maximal subgroup but is not of the form where the quotient acts via multiplication by .