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Volume 39 Number 3 Volume 39 Number 4 Volume 39 Number 5

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Research articles

ScienceAsia 39(2013): 436-439 |doi: 10.2306/scienceasia1513-1874.2013.39.436

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 sk be the number of elements of order k in G. Let nse(G)={sk | 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 GL3(4).

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School of Science, Sichuan University of Science & Engineering, Zigong Sichuan, 643000, China

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

Received 7 Nov 2012, Accepted 18 Jun 2013