The probability of an automorphism of an abelian group fixing a group element
Keywords:Fusion classes, Probability, Automorphisms
In this paper, we consider the probability of an automorphism of a finite abelian group fixing a group element. Explicit computations are made to find the fusion classes of a finite abelian groups. The probability of an automorphism fixing a group element is obtained in terms of fusion classes. We also compute the bounds of the probability for some particular cases.
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