Groups whose elements have given orders
For a finite group \(G\), let \(\pi_e(G)\) be the set of all orders of elements in \(G\) and \(h(G)=h(\pi_e(G))\) be the number of non-isomorphic groups \(H\) such that \(\pi_e(H)=\pi_e(G)\). The author gives a survey of results, obtained mostly by himself, concerning the question: For which finite groups \(G\) is \(h(G)\) finite, infinite, equal to 1?
scientific article; zbMATH DE number 1159088
scientific article