Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4650586 | Discrete Mathematics | 2008 | 7 Pages |
Abstract
In the present note, we investigate schemes S in which each element s satisfies ns⩽2ns⩽2 and ns*s≠2ns*s≠2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G//〈t〉G//〈t〉, where G is a finite group and t an involution of G weakly closed in CG(t)CG(t).Groups G with an involution t weakly closed in CG(t)CG(t) have been described in Glauberman's Z*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.
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Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mikhail Muzychuk, Paul-Hermann Zieschang,