Which finite simple groups are unit groups?
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We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order 2^k −1 for some k; or (c) a projective special linear group PSLn(F2) for some n ≥ 3. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups G with no non-trivial normal 2-subgroup.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Pure and Applied Algebra |
Vol/bind | 218 |
Udgave nummer | 4 |
Sider (fra-til) | 743-744 |
Antal sider | 2 |
ISSN | 0022-4049 |
DOI | |
Status | Udgivet - 2014 |
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