A characterization of groups of exponent
which are nilpotent of class at most 2
Abstract
Let
be a group of prime exponent
. In this paper we prove that
is nilpotent of class at most 2 if and only if one of the following properties is true:
is also the support of a commutative group
such that
and
have the same cyclic cosets [cosets of order
].
the operation
defined on
by putting
, gives
a structure of commutative group.\end
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DOI Code:
10.1285/i15900932v30n2p149
Keywords:
nilpotent groups; group partition
Full Text: PDF