Relative autocommutativity degree for topological groups

Document Type : Original Article

Author

Department of Mathematics, University of Qom, Qom, Iran

Abstract

Let G be a compact Hausdorff topological group with automorphism group Aut(G), which itself is a compact Hausdorff topological group. Suppose that H is a closed subgroup of G. In this paper, using Haar measure, we define the concept of relative autocommutativity degree Pr_A(H) for subgroup H which generalizes this concept for finite groups. We obtain some properties of Pr_A(H) which are analogous to the case of finite groups. In particular, we provide an upper bound for the relative autocommutativity degree of a non-abelian subgroup H and characterize the structural properties of H when this bound is attained.

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References

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Measure Algebras and Applications
Volume 3, Issue 2 - Serial Number 5
December 2025
Pages 37-45

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