The probability of an automorphism of an abelian group fixing a group element

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2021-4513

Keywords:

Fusion classes, Probability, Automorphisms

Abstract

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.

Author Biography

Harsha Arora, Government College Hansi.

Dept. of Mathematics.

References

H. Arora and R. Karan, “Groups as the union of fusion classes”, Note di matematica, vol. 35, no. 1, pp. 57-65, 2015. https://doi.org/10.1285/i15900932v35n1p57

H. Arora and R. Karan, “What is the probability of an automorphism fixes a group element?”, Communications in algebra, vol. 45, no. 3, pp. 1141-1150, 2017. https://doi.org/10.1080/00927872.2016.1206346

W. H. Gustafson, “What is the probability that two group elements commute?”, The American mathematical monthly, vol. 80, no. 9, pp. 1031-1034, 1973. https://doi.org/10.2307/2318778

R. K. Nath and A. K. Das, “On a lower bound of commutativity degree”, Rendiconti del Circolo Matematico di Palermo, vol. 59, no. 1, pp. 137-142, 2010. https://doi.org/10.1007/s12215-010-0010-6

G. Sherman, “What is the Probability an automorphism fixes a group element?”, The American mathematical monthly, vol. 82, no. 3, pp. 261-264, 1975. https://doi.org/10.2307/2319852

G. J. Sherman, Finite abelian groups in which the probability of an automorphism fixing an element is large, Mathematical Sciences Technical Reports no. 78, Mar. 1991 [Online]. Available: https://bit.ly/2W4QKkN

Published

2021-04-19 — Updated on 2021-07-26

How to Cite

[1]
H. Arora, “The probability of an automorphism of an abelian group fixing a group element”, Proyecciones (Antofagasta, On line), vol. 40, no. 4, pp. 1001-1010, Jul. 2021.

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Section

Artículos