Shi, J., Wu, Z., Hou, R. (2017). On the type of conjugacy classes and the set of indices of maximal subgroups. Bulletin of the Iranian Mathematical Society, 43(3), 867-874.

J. Shi; Z. Wu; R. Hou. "On the type of conjugacy classes and the set of indices of maximal subgroups". Bulletin of the Iranian Mathematical Society, 43, 3, 2017, 867-874.

Shi, J., Wu, Z., Hou, R. (2017). 'On the type of conjugacy classes and the set of indices of maximal subgroups', Bulletin of the Iranian Mathematical Society, 43(3), pp. 867-874.

Shi, J., Wu, Z., Hou, R. On the type of conjugacy classes and the set of indices of maximal subgroups. Bulletin of the Iranian Mathematical Society, 2017; 43(3): 867-874.

On the type of conjugacy classes and the set of indices of maximal subgroups

^{1}School of Mathematics and Information Science, Yantai University, Yantai 264005, China.

^{2}Xingjian College of Science and Liberal Arts, Guangxi University, Nanning 530004, China.

Abstract

Let $G$ be a finite group. By $MT(G)=(m_1,\cdots,m_k)$ we denote the type of conjugacy classes of maximal subgroups of $G$, which implies that $G$ has exactly $k$ conjugacy classes of maximal subgroups and $m_1,\ldots,m_k$ are the numbers of conjugates of maximal subgroups of $G$, where $m_1\leq\cdots\leq m_k$. In this paper, we give some new characterizations of finite groups by the type of conjugacy classes of maximal subgroups. By $\pi_t(G)$ we denote the set of indices of all maximal subgroups of $G$. We also investigate the influence of the set of indices of all maximal subgroups on the structure of finite groups.

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