Characterization of some finite groups by prime order element graph

Momen, Zahra

doi:10.22061/jdma.2025.12206.1142

Characterization of some finite groups by prime order element graph

Document Type : Full Length Article

Author

Zahra Momen

Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, I. R. Iran.

10.22061/jdma.2025.12206.1142

Abstract

For a finite group G, the prime order element graph of G, is defined as follows: the vertex set is the elements of G and two distinct vertices a and b are adjacent if and only if order of ab is prime. This graph is denoted by γ(G). In this paper, we prove that the alternating groups A₄ and A₅, all groups of order pq, where p and q are prime numbers, and cyclic groups Z_p of prime order are uniquely characterized by the prime order element graph.

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