OD-Characterization of the Symmetric Group S₄₉

Abstract:

The degree pattern of a finite group G associated with its prime graph has been 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 |G|=|H| and D(G)=D(H).Moreover, a 1-fold OD-characterizable group is simply called an OD-characterizable group. In this paper, we will show that the symmetric group S₄₉ can be characterized by its order and degree pattern. In fact, the symmetric group S₄₉ is 3-fold OD-characterizable

• Periodical: Advanced Materials Research (Volumes 535-537)
• Pages: 2596-2599
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.535-537.2596
• Online since: June 2012
• Authors: Yan Xiong Yan
• Keywords: Almost Simple Group, Degree of a Vertex, Degree Pattern, Finite Group, Prime Graph

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