Which finite simple groups are unit groups?
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Submitted manuscript, 212 KB, PDF document
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.
Original language | English |
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Journal | Journal of Pure and Applied Algebra |
Volume | 218 |
Issue number | 4 |
Pages (from-to) | 743-744 |
Number of pages | 2 |
ISSN | 0022-4049 |
DOIs | |
Publication status | Published - 2014 |
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ID: 64393150