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 ...

Proceedings of the American Mathematical Society, Vol. 33, No. 2 (Jun., 1972), pp. 297-301 (5 pages) Let $G$ be a one-relator group having torsion. It is easy to show ...

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 ...