论文标题
关于不可用给定质量排除的群体和索引的产品
On products of groups and indices not divisible by a given prime
论文作者
论文摘要
让组$ g = ab $为子组$ a $ and $ b $的产物，让$ p $为素数。我们证明，$ p $不会将每个$ p $ p $ prime power Order $ x \ prime x \ x \ t in a \ cup b $的每个$ p $ regular emport of的偶联类别尺寸（索引）划分，并且仅当$ g $ as $ g $ as $ p $ -decomposable，即$ g = $ g = o_p（g）\ times o_ times o_ times o_ {p'}（g）（g）$。
Let the group $G = AB$ be the product of subgroups $A$ and $B$, and let $p$ be a prime. We prove that $p$ does not divide the conjugacy class size (index) of each $p$-regular element of prime power order $x\in A\cup B$ if and only if $G$ is $p$-decomposable, i.e. $G=O_p(G) \times O_{p'}(G)$.
