OD-Characterization of the automorphism groups of O 10 ± (2)

Yanxiong Yan (), Guiyun Chen () and Lili Wang ()
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Yanxiong Yan: Southwest University
Guiyun Chen: Southwest University
Lili Wang: Chongqing University of Technology

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 3, 183-195

Abstract: Abstract The prime graph of a finite group was introduced by Gruenberg and Kegel. The degree pattern of a finite group G associated to its prime graph was introduced in [1] and denoted by D(G). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions (1) |G| = |H| and (2) D(G) = D(H). Moreover, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Till now a lot of finite simple groups were shown to be OD-characterizable, and also some finite groups especially the automorphism groups of some finite simple groups were shown not being OD-characterizable but k-fold OD-characterizable for some k > 1. In the present paper, the authors continue this topic and show that the automorphism groups of orthogonal groups O 10 + (2) and O 10 − (2) are OD-characterizable.

Keywords: Prime graph; degree pattern; degree of a vertex; order component (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0011-6

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