Year: 2025
Type: article
Abstract: Suppose that $x$, $y$ are elements of a finite group $G$ lying in conjugacy classes of coprime sizes. We prove that $\langle {x^G} \cap {y^G}\rangle$ is an abelian normal subgroup of $G$ and, as a consequence, that if $x$ and $y$ are $π$-regular elements for some set of primes $π$, then $x^G y^G$ is a $π$-regular conjugacy class in $G$. The latter statement was previously known for $π$-separable groups $G$ and this generalisation permits us to extend several results concerning the common divisor graph on $p$-regular conjugacy classes, for some prime $p$.
Source: Apollo (University of Cambridge)
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891809072
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