A new characterization of  PSL(3,q)

Soleyman Asgary

doi:10.5269/bspm.39391

Soleyman Asgary Imam-Ali University

Abstract

Let G be a group. In this paper, we prove that G is isomorphic to PSL(3,q) if and only if |G|=|PSL(3,q)| and m(G)=m(PSL(3,q)), where q is a prime power and m(G) is the maximal order of elements in G.

Downloads

Download data is not yet available.

References

S. Asgary and N. Ahanjideh, nse characterization of some finite simple groups, Scientific Annals of ”Al. I. Cuza”3 (2), 797-806, (2016).

S. Asgary and N. Ahanjideh, Characterization of PSL(3, q) by nse, Mathematical Reports 19 (69) No 4, 425-438, (2017).

J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, Atlas of finite groups, Clarendon Press, New York, (1985).

G. Y. Chen, On Frobenius and 2-Frobenius group, J. Southwest China Normal Univ, 20(5), 485-487, (1995).

G. Y. Chen, Futher refelections on Thompson’s conjecture, J. Algebra, 218(1), 276-285, (1999).

W. Feit, On large Zsigmondy primes, Proc. Amer. Math. Soc., 102 (1), 29-33, (1988).

A. Iranmanesh, S. H. Alavi and B. Khosravi, A characterization of PSL(3, q), where q is an odd prime power, J. Pure Appli. Algebra, 170, 243-254, (2002).

A. Iranmanesh, S. H. Alavi and B. Khosravi, A characterization of PSL(3, q) for q = 2m, Acta Mathematica Sinica, English Series, 18(3), 463-472, (2002).

A. S. Kondratev and V. D. Mazarove, Recognition of Alternating groups of prime degree from their element orders, Siberian Math. J., 41 (2), 294-302, (2000).

J. Li, D. Yu, G. Chen and W. Shi, A characterization of simple K4-groups of type L2(q) and their automorphism groups, Iranian Mathematical Society, 43, No. 2, 501-514, (2017).

J.B. Li, W.J. Shi and D.P. Yu, A characterization of some PGL(2, q) by maximum element orders, Bull Korean Math. Soc. 52, No. 6, 2025-2034, (2015).

V.D. Mazurov and G.Y. Chen, Recognizability of finite simple groups L4(2m) and U4(2m) by spectrum, Algebra and Logic, 47, No. 1, 49-55, (2008).

J. S. Williams, Prime graph components of finite groups, J. Algebra, 69, 487-513, (1981).

A. V. Zavarnitsine, Recognition of the simple L3(q) by element orders, J. Group Theory, 7, 81-97, (2004).

Q. Zhang and W. Shi, A new characterization of simple K3-groups and some L2(p), J. Algebra Colloquium, 20(3), 361-368, (2013).