Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 201-207, 2022
On the conjugate type vector and the structure of a normal subgroup
Ruifang Chen, Lujun Guo
Received September 14, 2020. Published online November 18, 2021.
Abstract: Let $N$ be a normal subgroup of a group $G$. The structure of $N$ is given when the $G$-conjugacy class sizes of $N$ is a set of a special kind. In fact, we give the structure of a normal subgroup $N$ under the assumption that the set of $G$-conjugacy class sizes of $N$ is $(p_{1n_1}^{a_{1n_1}},\cdots, p_{1 1}^{a_{11}}, 1) \times\cdots\times(p_{rn_r}^{a_{rn_r}},\cdots, p_{r1}^{a_{r1}}, 1)$, where $r>1$, $n_i>1$ and $p_{ij}$ are distinct primes for $i\in\{1, 2, \cdots, r\}$, $j\in\{1, 2, \cdots, n_i\}$.
Affiliations: Ruifang Chen (corresponding author), Lujun Guo, College of Mathematics and Information Science, Henan Normal University, Changsha City Peach Lake Road 15, Xinxiang, Henan, P. R. China, 453007, e-mail: fang119128@126.com, lujunguo0301@163.com
