Institution: | aDepartment of Mathematics, Netanya Academic College, 42365 Netanya, Israel bDepartment of Mathematics, University of Texas at Brownsville, Brownsville, TX 78520, USA |
Abstract: | In the present note, we investigate schemes S in which each element s satisfies ns 2 and ns*s≠2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G// t , where G is a finite group and t an involution of G weakly closed in CG(t).Groups G with an involution t weakly closed in CG(t) have been described in Glauberman's Z*-Theorem G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403–420] with the help of the largest normal subgroup of G having odd order. |