On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes
Copyright policy )On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes
The greatest power of a prime $p$ dividing the natural number $n$ will be denoted by $n_p$. Let $Ind_G(g)=|G:C_G(g)|$. Suppose that $G$ is a finite group and $p$ is a prime. We prove that if there exists an integer $\alpha>0$ such that $Ind_G(a)_p\in \{1,p^{\alpha}\}$ for every $a$ of $G$ and a $p$-element $x\in G$ such that $Ind_G(x)_p>1$, then $G$ includes a normal $p$-complement.
- Siberian Federal University Russian Federation
normal \(p\)-complement, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory, Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, conjugacy classes
normal \(p\)-complement, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory, Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, conjugacy classes
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