The groupoid of 0-reduced varieties of Semigroups (n).
Let be a group and a prime. The subgroup generated by the elements of order different from is called the Hughes subgroup for exponent . Hughes [3] made the following conjecture: if is non-trivial, its index in is at most . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case and arbitrary, and that of Hogan and Kappe [2] concerning the case when is metabelian, and arbitrary. A common proof is...