Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 3: 541 - 553

DOI: https://doi.org/10.1007/s11464-010-0011-y

Research articles

Recognizing alternating groups A p +3 for certain primes p by their orders and degree patterns

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  • 1.Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran; 2.Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran；School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran;

Published date: 05 Sep 2010

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Abstract

The degree pattern of a finite group M has been introduced by A. R. Moghaddamfar et al. [Algebra Colloquium, 2005, 12(3): 431―442]. A group M is called k-fold OD-characterizable if there exist exactly k nonisomorphic finite groups having the same order and degree pattern as M. In particular, a 1-fold OD-characterizable group is simply called OD-characterizable. In this article, we will show that the alternating groups Ap+3 for p = 23, 31, 37, 43 and 47 are OD-characterizable. Moreover, we show that the automorphism groups of these groups are 3-fold OD-characterizable. It is worth mentioning that the prime graphs associated with all these groups are connected.

Key words： OD-characterization of finite group; degree pattern; prime graph; alternating and symmetric groups

Cite this article

A. A. HOSEINI, A. R. MOGHADDAMFAR, . Recognizing alternating groups A p +3 for certain primes p by their orders and degree patterns[J]. Frontiers of Mathematics in China, 2010 , 5(3) : 541 -553 . DOI: 10.1007/s11464-010-0011-y

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