Let $G$ be a CP-group and $|G|={p_1}^{n_1}…{p_k}^{n_k}$ that $p_i$'s are distinct primes and $n_i>0$. Also $V_i=\{g\in {G};o(g)|{p_i}^{n_i}\}$, $1≤i≤k$.
- What is $|V_i|$?
- There are $V_i $ and $V_j$ that $| V_i |=| V_j |,i≠j$.
Let $G$ be a CP-group and $|G|={p_1}^{n_1}…{p_k}^{n_k}$ that $p_i$'s are distinct primes and $n_i>0$. Also $V_i=\{g\in {G};o(g)|{p_i}^{n_i}\}$, $1≤i≤k$.
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