A sufficient conditon for solvability of finite groups

Wujie Shi

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arXiv · 1704.01487

A sufficient conditon for solvability of finite groups

Wujie Shi

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Abstract

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

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Wujie Shi. 2017-04-05. A sufficient conditon for solvability of finite groups. https://arxiv.org/abs/1704.01487

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