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On the Minimal Parabolic System Related to M24

On the Minimal Parabolic System Related to M24,10.1112/jlms/s2-40.1.40,Journal of The London Mathematical Society-second Series,P. Rowley

On the Minimal Parabolic System Related to M24   (Citations: 10)
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    • ...and mwwmwwm= = = = t m have been studied in [R1, R2], respectively...
    • ...The arguments we use are piecewise quite elementary, almost self-contained, and are in the spirit of earlier work in [R1, R2]...
    • ...We begin this section with some properties of L3(2) and S 6 (for a construction of S 6 consult Section 2 of [R1])...
    • ...Proof. For the subgroup lattice see Fig. 1 and (3.22) of [R1] and for part (i) consult (3.10)(i) and (3.18) of [R1]...
    • ...Proof. For the subgroup lattice see Fig. 1 and (3.22) of [R1] and for part (i) consult (3.10)(i) and (3.18) of [R1]...
    • ...Proof. For the subgroup lattice see Fig. 1 and (3.22) of [R1] and for part (i) consult (3.10)(i) and (3.18) of [R1]. The main theorem of [R1] establishes (ii)...
    • ...Parts (iii) and (iv) are proved in (3.3)(i) and (3.11) of [R1], respectively...
    • ...Assume that X is a normal 2-subgroup of Pi and that Y=X & X xj \S. Then Y & Y xi \Pij . Proof. (i) See (2.1) (ii) of [R1]...
    • ...Proof. From [R1, (2.2); R2, Lemma 2.3], we obtain parts (i) and (ii)...
    • ...Part (iii) results from [R2, Lemma 2.3; R1, (2.4)] (note that xo=x1=a and yo= y1=b where a and b are as in [R1, (2.3)])...
    • ...Part (iii) results from [R2, Lemma 2.3; R1, (2.4)] (note that xo=x1=a and yo= y1=b where a and b are as in [R1, (2.3)])...

    Peter Rowley. On the Minimal Parabolic System Related to the Monster Simple Group

    • ...According to [Tim3] the semiclassical diagrams of rank three correspond to diagrams ,o r . For the latter according to [Hei2] and [Row] we have GÅ He;M24 or 3 7 Sp6Ö2Ü...

    A. Fukshanskyet al. The Semiclassical Parabolic Systems

    • ...and [Row] a semiclassical parabolic system with diagram has as group one of the following: , 24 or 3 7 6 2 . In the first two cases 2 10 whereas 2 9 in the third...

    A. Fukshanskyet al. Semiclassical Parabolic Systems Related to M 24

    • ...It was shown in [14] that if n = 3 and Rza/Oz(Rz3 ) -_ 3. S 6 then the order of B is either 29 or 21°...

    A. A. Ivanovet al. An infinite family of simply connected flag-transitive tilde geometrie...

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