Let $G$ be a finite group of order divisible by the prime $p$. It is shown that the number of elements of $G$ of order $p$ is congruent to $-1$ modulo $p^2$, unless a ...

This is a preview. Log in through your library . Abstract Let G be a finite group, p a prime, and x a p-element in G. An element g in G is called a witness of G if the subgroup generated by x and g is ...

Group theory serves as a fundamental language for describing symmetry in both mathematics and physics. Finite groups, defined by their limited number of elements, are central to modern algebra and ...