E. Artin. The orders of the classical simple groups. Commun. Pure Appl. Math. 8 (1955), 455-472. Home/Search Document Not in Database Summary Related Articles Check |
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Reconstructing Simple Group Actions - Kantor, Penttila (Correct)
....Output: A set and an action of G as required in Theorem 2.3. Call ALT ORDER. If G = A r for some r, call ALT1 and then ALT2. Let p be the prime contributing the largest prime power to jGj, except when jGj = jPSU(4; 2)j and n 6= 40, in which case let p = 2. Then p is the characteristic of G [Ar]. If p fi fi n call CLASSICAL NS (Section 5) producing a new set Omega 0 . Here Omega is a G orbit of nonsingular subspaces, and CLASSICAL NS produces the set Omega 0 of isotropic or singular points of an underlying vector space. Now p6 fi fi n. Call PSL ORDER (Section 4) If G = ....
....i ) r 1 Gamma (r 1)2 Gammam Gamma m r Gamma m Gamma 1: Thus, if G = A r then k = jGj 2 1 is between r Gamma 1 and r Gamma log 2 r Gamma 1, and the indicated procedure finds r. 8 W. M. Kantor and T. Penttila Suppose that the procedure determines that jGj = r =2 for some r. By [Ar], G is isomorphic to A r or PSL(3; 4) If jGj = jPSL(3; 4)j = jA 8 j then G = A 8 by Hypothesis 2.1(a,b) and the procedure correctly decides that G is not an alternating group. ALT1 Input: G Sym( Omega Gamma permutation isomorphic to the action of A r , r 9, on the set of all subsets ....
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E. Artin, The orders of the classical simple groups. Comm. Pure Appl. Math. 8 (1955) 455--472.
Black-box recognition of finite simple groups of.. - Babai, Kantor.. (1 citation) (Correct)
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E. Artin. The orders of the classical simple groups. Commun. Pure Appl. Math. 8 (1955), 455-472.
uber einem quadratisch abgeschlossenen Korper - Der Charakteristik Geom (Correct)
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E. Artin, The orders of the classical simple groups, Comm. Pure Appl. Math. 8 (1955), 455--472.
Notes on Classical Groups - Cameron (Correct)
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E. Artin, The orders of the classical simple groups, Comm. Pure Appl. Math. 8 (1955), 455--472.
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