ON THE RELATION BETWEEN THE NON-COMMUTING GRAPH AND THE PRIME GRAPH

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AHANJIDEH N.; IRANMANESH A.

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Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2012 | Volume:1 | Issue:1 Page(s): 25-28

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Information Journal Paper

Title

ON THE RELATION BETWEEN THE NON-COMMUTING GRAPH AND THE PRIME GRAPH

Author(s)

AHANJIDEH N. | IRANMANESH A. | Issue Writer Certificate

Keywords

NON-COMMUTING GRAPHQ4

PRIME GRAPHQ4

MAXIMAL ABELIAN SUBGROUPSQ4

MAXIMAL INDEPENDENT SET OF THE GRAPHQ4

Abstract

Given a non-abelian finite group G, let p (G) denote the set of prime divisors of the order of G and denote by Z (G) the center of G. The PRIME GRAPH of G is the graph with vertex set p (G) where two distinct primes p and q are joined by an edge if and only if G contains an element of order pq and the NON-COMMUTING GRAPH of G is the graph with the vertex set G-Z (G) where two non-central elements x and y are joined by an edge if and only if xy ¹ yx. Let G and H be non-abelian finite groups with isomorphic NON-COMMUTING GRAPHs. In this article, we show that if |Z (G)| = |Z (H)|, then G and H have the same PRIME GRAPHs and also, the set of orders of the MAXIMAL ABELIAN SUBGROUPS of G and H are the same.

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APA: Copy

AHANJIDEH, N., & IRANMANESH, A.. (2012). ON THE RELATION BETWEEN THE NON-COMMUTING GRAPH AND THE PRIME GRAPH. INTERNATIONAL JOURNAL OF GROUP THEORY, 1(1), 25-28. SID. https://sid.ir/paper/212632/en

Vancouver: Copy

AHANJIDEH N., IRANMANESH A.. ON THE RELATION BETWEEN THE NON-COMMUTING GRAPH AND THE PRIME GRAPH. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2012;1(1):25-28. Available from: https://sid.ir/paper/212632/en

IEEE: Copy

N. AHANJIDEH, and A. IRANMANESH, “ON THE RELATION BETWEEN THE NON-COMMUTING GRAPH AND THE PRIME GRAPH,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 1, no. 1, pp. 25–28, 2012, [Online]. Available: https://sid.ir/paper/212632/en

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