A characterization of groups of exponent p which are nilpotent of class at most 2


Let (\mathbf{G},+) be a group of prime exponent p = 2n + 1. In this paper we prove that (\mathbf{G},+) is nilpotent of class at most 2 if and only if one of the following properties is true: 
i) \mathbf{G} is also the support of a commutative group (\mathbf{G},+') such that (\mathbf{G},+) and (\mathbf{G},+') have the same cyclic cosets [cosets of order p].     ii) the operation \oplus defined on \mathbf{G} by putting x \oplus y = x/2 + y + x/2, gives \mathbf{G} a structure of commutative group.\end

DOI Code: 10.1285/i15900932v30n2p149

Keywords: nilpotent groups; group partition

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