论文标题
最大循环亚组的结合类别
Conjugacy classes of maximal cyclic subgroups
论文作者
论文摘要
在本文中，我们将$η（g）$设置为$ g $的最大循环亚组的结合类数量。我们考虑$η$以及直接和半独立产品。我们表征了普通子组$ n $，因此$η（g/n）=η（g）$。我们在g \ mid \ langle g \ rangle {\ rm〜是〜maximal〜cyclic} \} $中设置$ g^ - = \ {g \ { We show if $\langle G^- \rangle < G$, then $G/\langle G^- \rangle$ is either (1) an elementary abelian $p$-group for some prime $p$, (2) a Frobenius group whose Frobenius kernel is a $p$-group of exponent $p$ and a Frobenius complement has order $q$ for distinct primes $p$ and $ q $，或（3）同构至$ a_5 $。
In this paper, we set $η(G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$. We consider $η$ and direct and semi-direct products. We characterize the normal subgroups $N$ so that $η(G/N) = η(G)$. We set $G^- = \{ g \in G \mid \langle g \rangle {\rm ~is~not ~maximal~cyclic} \}$. We show if $\langle G^- \rangle < G$, then $G/\langle G^- \rangle$ is either (1) an elementary abelian $p$-group for some prime $p$, (2) a Frobenius group whose Frobenius kernel is a $p$-group of exponent $p$ and a Frobenius complement has order $q$ for distinct primes $p$ and $q$, or (3) isomorphic to $A_5$.
