Groups in which prime order elements commute

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Presidency University Kolkata, India

Abstract

It is known that if $G$ is a finite group in which all the elements of prime power order commute, then $G$ is abelian. However, the same does not hold if prime power is replaced by prime. In this article, we introduce the study of a class of finite groups $G$ in which the prime order elements commute. In particular, we discuss the relationship between these class of groups with other known classes of finite groups, like simple groups, perfect groups etc. Moreover, we also prove some results on the possible orders of such groups. Finally, we conclude with some open issues and observations supported by computational evidences using GAP.

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References

[1] K. Conrad, Supgroup series II, Lecture Notes available at https://kconrad.math.uconn.edu/blurbs/grouptheory/subgpseries2.pdf.
[2] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.12.2 ; 2022, https://www.gap-system.org.
[3] D. Gorenstein, Finite groups, AMS Chelsea Publishing, New York, 1968.
[4] D. J. S. Robinson, A course in the theory of groups, 2nd Edition, Graduate Text in Mathematics, Springer, New York, 1996.
[5] M. Suzuki, Group theory I, Springer Berlin, Heidelberg, 1982.
International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 13 April 2025

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History

  • Receive Date: 02 January 2025
  • Revise Date: 11 March 2025
  • Accept Date: 13 March 2025
  • Published Online: 13 April 2025

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