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Keywords:
index; conjugacy class size; Baer group
index; conjugacy class size; Baer group
Summary:
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 $i\in \{1, 2, \cdots , r\}$, $j\in \{1, 2, \cdots , n_i\}$.
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