Which finite simple groups are unit groups?
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Which finite simple groups are unit groups? / Davis, Christopher James; Occhipinti, Tommy.
I: Journal of Pure and Applied Algebra, Bind 218, Nr. 4, 2014, s. 743-744.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Which finite simple groups are unit groups?
AU - Davis, Christopher James
AU - Occhipinti, Tommy
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
U2 - 10.1016/j.jpaa.2013.08.013
DO - 10.1016/j.jpaa.2013.08.013
M3 - Journal article
VL - 218
SP - 743
EP - 744
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 4
ER -
ID: 64393150