Shelah's Singular Compactness Theorem.
It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.
In questo lavoro studiamo i non CC-gruppi monolitici con tutti i quozienti propri CC-gruppi, che hanno sottogruppi abeliani normali non banali.
In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.
Simple quasigroups with commuting inner permutations are medial.
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .