OD-characterization of some alternating groups (Q2813407)

Let \(G\) be a finite group and \(\Gamma(G)\) be its prime graph. The degree pattern \(D(G)\) of \(G\) is defined in [\textit{A. R. Moghaddamfar} et al., Algebra Colloq. 12, No. 3, 431--442 (2005; Zbl 1072.20015)]. A finite group \(G\) is called OD-characterizable if there exist exactly a non-isomorphic finite groups with the same order and the same degree pattern as \(G\) . We set \(s(G)\) to denote the number of connected components of the prime graph \(\Gamma(G)\). In this note the author give a OD-characterization of \(A_{p+3}\) except \(A_10\) with \(s(A_{p+3})\) =1.