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- Title
On the prime graph of PSL(2, p) where p > 3 is a prime number.
- Authors
Khosravi, Bahman; Khosravi, Behnam; Khosravi, Behrooz
- Abstract
Let G be a finite group. We define the prime graph Γ( G) as follows. The vertices of Γ( G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. Recently M. Hagie [5] determined finite groups G satisfying Γ( G) = Γ( S), where S is a sporadic simple group. Let p > 3 be a prime number. In this paper we determine finite groups G such that Γ( G) = Γ( PSL(2, p)). As a consequence of our results we prove that if p > 11 is a prime number and p ≢ 1 (mod 12), then PSL(2, p) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.
- Subjects
PRIME numbers; NATURAL numbers; FINITE groups; GROUP theory; MODULES (Algebra)
- Publication
Acta Mathematica Hungarica, 2007, Vol 116, Issue 4, p295
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-007-6021-x