The finite groups with no real \(p\)-elements.
The authors use the classification of finite simple groups to investigate finite groups satisfying the condition of the title, where \(p\) is an odd prime. They look in detail at the case when \(G\) is a simple group, providing a specific list of groups in this case. They use this to obtain also more general results. They prove that if \(G\) is a finite group with no non-trivial quotients of odd order, \(p\) is any odd prime dividing the order of \(G\) and \(G\) has no real elements of order \(p\), then \(G\) is not \(p\)-solvable and \(G\) has Abelian Sylow \(p\)-subgroups. In addition, the special cases when \(p=3\) and \(p=5\) are treated in more detail.
scientific article; zbMATH DE number 6135119