A sufficient conditon for solvability of finite groups

2017/04/05 by Wujie Shi, Shi, Wujie
Mathematics · #20D10 #20D60 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D10 #msc:20D60

paper · pdf · doi:10.48550/arxiv.1704.01487

5 pages

arxiv created 2017/04/05 · arxiv updated 2017/04/06

Abstract

The following theorem is proved: Let G be a finite group and π_e(G) be the set of element orders in G. If π_e(G) ∩ \2\=∅; or π_e(G) ∩ \3, 4\=∅; or π_e(G) ∩ \3,5\=∅, then G is solvable. Moreover, using the intersection with π_e(G) being empty set to judge G is solvable or not, only the above three cases.

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