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On Thompson’s Conjecture for Alternating Groups Ap+3
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-22
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Let G be a group.
Denote by π(G) the set of prime divisors of |G|.
Let GK(G) be the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p·q.
We set s(G) to denote the number of connected components of the prime graph GK(G).
Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G.
Alavi and Daneshkhah proved that the groups, An where n=p,p+1,p+2 with s(G)≥2, are characterized by N(G).
As a development of these topics, we will prove that if G is a finite group with trivial center and N(G)=N(Ap+3) with p+2 composite, then G is isomorphic to Ap+3.
American Psychological Association (APA)
Liu, Shitian& Yang, Yong. 2014. On Thompson’s Conjecture for Alternating Groups Ap+3. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1050914
Modern Language Association (MLA)
Liu, Shitian& Yang, Yong. On Thompson’s Conjecture for Alternating Groups Ap+3. The Scientific World Journal No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1050914
American Medical Association (AMA)
Liu, Shitian& Yang, Yong. On Thompson’s Conjecture for Alternating Groups Ap+3. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1050914
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050914