On the conjugate type vector and the structure of a normal subgroup

Chen, Ruifang, and Guo, Lujun. "On the conjugate type vector and the structure of a normal subgroup." Czechoslovak Mathematical Journal 72.1 (2022): 201-207. <http://eudml.org/doc/298156>.

@article{Chen2022,
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 \lbrace 1, 2, \cdots , r\rbrace $, $j\in \lbrace 1, 2, \cdots , n_i\rbrace $.},
author = {Chen, Ruifang, Guo, Lujun},
journal = {Czechoslovak Mathematical Journal},
keywords = {index; conjugacy class size; Baer group},
language = {eng},
number = {1},
pages = {201-207},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the conjugate type vector and the structure of a normal subgroup},
url = {http://eudml.org/doc/298156},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Chen, Ruifang
AU - Guo, Lujun
TI - On the conjugate type vector and the structure of a normal subgroup
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 1
SP - 201
EP - 207
AB - 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 \lbrace 1, 2, \cdots , r\rbrace $, $j\in \lbrace 1, 2, \cdots , n_i\rbrace $.
LA - eng
KW - index; conjugacy class size; Baer group
UR - http://eudml.org/doc/298156
ER -