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- W2150468910 abstract "Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p′ are joined by an edge if there is an element in G of order pp′. In [G. Y. Chen et al., Recognition of the finite almost simple groups PGL 2 (q) by their spectrum, Journal of Group Theory, 10 (2007) 71–85], it is proved that PGL(2, p k ), where p is an odd prime and k > 1 is an integer, is recognizable by its spectrum. It is proved that if p > 19 is a prime number which is not a Mersenne or Fermat prime and Γ(G) = Γ(PGL(2, p)), then G has a unique nonabelian composition factor which is isomorphic to PSL(2, p). In this paper as the main result, we show that if p is an odd prime and k > 1 is an odd integer, then PGL(2, p k ) is uniquely determined by its prime graph and so these groups are characterizable by their prime graphs." @default.
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- W2150468910 date "2010-11-01" @default.
- W2150468910 modified "2023-10-04" @default.
- W2150468910 title "CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p<sup>k</sup>) WHERE p AND k > 1 ARE ODD" @default.
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- W2150468910 doi "https://doi.org/10.1142/s021819671000587x" @default.
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