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On the autocommutator subgroup
by
Mihai Chis
West University of Timisoara, Faculty of Mathematics and Computer Sciences
Coauthors: Codruta Chis,
Banat University of Agricultural Sciences, Faculty of Agricultural Management
The autocommutator subgroup is an important characteristic subgroup of a group. We show that there are finite groups not isomorphic with the autocommutator subgroup of any group. We determine in certain cases the autocommutator subgroup of a direct product of groups. We show that for a finite nilpotent group any odd prime divisor of the order of the group divides the order of the autocommutator subgroup. We prove this wrong for the prime 2, but also generally for nonnilpotent groups. We also study groups whose autocommutator subgroup is a p-group.
Date received: April 28, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-36.