Groups with elementary abelian commutant of at most p 2th order
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We obtain a representation of nilpotent groups with a commutant of the type (p) or (p, p) that has the form of a product of two normal subgroups. One of these subgroups is constructively described as a Chernikov p-group of rank 1 or 2, and the other subgroup has a certain standard form. We also obtain a representation of nonnilpotent groups with a commutant of the type (p) or (p, p) in the form of a semidirect product of a normal subgroup of the type (p) or (p, p) and a nilpotent subgroup with a commutant of order p or 1.
KeywordsNormal Subgroup Direct Product Finite Group Cyclic Group Nilpotent Group
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