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<p>We study bijections of a group onto itself that commute with distinguished subgroups of its automorphismsand establish the general structure of such groups of bijections.We obtain the structure of these groups of bijections as the structure of the centralizer ofa subgroup of the permutation group of a set of arbitrary cardinality.In particular, we show thatthe centralizer of the regular representation of a group on itselfis isomorphic to the group itself.Using the structure of such bijection groupsfor the free two-generated Burnside group of exponent 3,we compute the group of its bijections commuting with its inner automorphisms.</p>

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Bijections of a Group Which Commute with Its Automorphisms

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • O. V. Bryukhanov

摘要

We study bijections of a group onto itself that commute with distinguished subgroups of its automorphismsand establish the general structure of such groups of bijections.We obtain the structure of these groups of bijections as the structure of the centralizer ofa subgroup of the permutation group of a set of arbitrary cardinality.In particular, we show thatthe centralizer of the regular representation of a group on itselfis isomorphic to the group itself.Using the structure of such bijection groupsfor the free two-generated Burnside group of exponent 3,we compute the group of its bijections commuting with its inner automorphisms.