NSE characterization of some alternating groups

作者：Ahanjideh Neda^*; Asadian Bahareh

来源：Journal of Algebra and Its Applications, 2015, 14(2): 1550012.

DOI：10.1142/S0219498815500127

• Set of the numbers of elements of the same order
• prime graph

Let p >= 5 be a prime and n is an element of {p, p + 1, p + 2}. Let G be a finite group and pi(e)(G) be the set of element orders of G. Assume that k is an element of pi(e)(G) and m(k)(G) is the number of elements of order k in G. Set nse(G) = {m(k)(G) : k is an element of pi(e)(G)}. In this paper, we show that if nse(A(n)) = nse(G), p is an element of pi(G) and p(2) inverted iota vertical bar G vertical bar, then G congruent to A(n). As a consequence of our result, we show that if nse(A(n)) = nse(G) and vertical bar G vertical bar = vertical bar A(n)vertical bar, then G congruent to A(n).

• 出版日期2015-3