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Groups with elementary abelian commutant of at most p 2th order

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    O. O. Mazurok

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  1. O. O. Mazurok
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 534–539, April, 1998.

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Mazurok, O.O. Groups with elementary abelian commutant of at most p 2th order. Ukr Math J 50, 605–611 (1998). https://doi.org/10.1007/BF02487392

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  • DOI: https://doi.org/10.1007/BF02487392

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