Abstract

Let G be a group and &omega(G) be the set of element orders of G. Let kє &omega(G) and s_k be the number of elements of order k in G. Let nse (G) = {s_k| k &omega(G) }. In Khatami et al. (2011) and Liu (2012c) the authors proved that L₃(2) and L₃₍)(4) are unique determined by nse (G). In this study, we prove that if G is a group such that nse (G) = nse (J₁), then G ≅ J₁.

Keywords:

Element order, Janko group, Number of elements of the same order, Thompson' problem,

References

Competing interests

The authors have no competing interests.

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The authors have no competing interests.