If ๐ is a class of groups, a group G is minimal non-๐ if it is not an ๐-group, but all its proper subgroups belong to ๐. The aim of this paper is to prove that for an infinite locally graded group, the property of being minimal non-hypercentral and that of being minimal non-hypercyclic are equivalent. Moreover, the main properties of infinite minimal non-hypercentral groups are described. In the last section, we study groups of infinite rank in which all proper subgroups of infinite rank satisfy a generalized supersolubility condition.
The aim of this paper is to show that the structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented.
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