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A characterization of L₃(4)

Shitian Liu

 
ABSTRACT:     Let G be a group and ω(G) be the set of element orders of G. Let k∈ω(G) and s_k be the number of elements of order k in G. Let nse(G)={s_k | k∈ω(G)}. L₃(2)≅L₂(7) is uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G)=nse(L₃(4)), then G≅L₃(4).

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* Corresponding author, E-mail: liust@suse.edu.cn

Received 7 Nov 2012, Accepted 18 Jun 2013