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searching for Maximal subgroup 32 found (50 total)

Dempwolff group (594 words) [view diff] exact match in snippet view article find links to article

sporadic group (the full automorphism group of this lattice) as a maximal subgroup. Huppert (1967, p.124) showed that any extension of G L n ( F q ) {\displaystyle

Monster group (2,972 words) [view diff] exact match in snippet view article find links to article

space over the field with 2 elements. A large subgroup H (preferably a maximal subgroup) of the Monster is selected in which it is easy to perform calculations

Thompson uniqueness theorem (144 words) [view diff] exact match in snippet view article find links to article

that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian subgroup of rank 3. Bender (1970)

McLaughlin sporadic group (807 words) [view diff] exact match in snippet view article find links to article

is a maximal subgroup of the Lyons group. McL has one conjugacy class of involution (element of order 2), whose centralizer is a maximal subgroup of type

Pauli–Lubanski pseudovector (2,044 words) [view diff] exact match in snippet view article find links to article

the generator of the little group of the Poincaré group, that is the maximal subgroup (with four generators) leaving the eigenvalues of the four-momentum

Suzuki sporadic group (495 words) [view diff] exact match in snippet view article find links to article

· Suz of the Suzuki group. This makes the group 6 · Suz · 2 into a maximal subgroup of Conway's group Co0 = 2 · Co1 of automorphisms of the Leech lattice

Tits group (720 words) [view diff] exact match in snippet view article find links to article

The Tits group occurs as a maximal subgroup of the Fischer group Fi22. The group 2F4(2) also occurs as a maximal subgroup of the Rudvalis group, as the

Feit–Thompson theorem (2,854 words) [view diff] exact match in snippet view article find links to article

CN-theorem and in the proof of the Feit–Thompson odd-order theorem. Each maximal subgroup M has a certain nilpotent Hall subgroup Mσ with normalizer contained

Gary Seitz (598 words) [view diff] exact match in snippet view article find links to article

groups, and as an application went a long way towards solving the maximal subgroup problem for finite groups. For this work he received the Creativity

Conway group Co1 (925 words) [view diff] exact match in snippet view article find links to article

contained in a maximal subgroup of type 211:M24. An image of an octad or 16-set has a centralizer of the form 21+8.O8+(2), a maximal subgroup. The smallest

Conway group Co2 (1,160 words) [view diff] exact match in snippet view article find links to article

Z/2Z × Co2 or Z/2Z × Co3. The Mathieu group M23 is isomorphic to a maximal subgroup of Co2 and one representation, in permutation matrices, fixes the type

Thompson sporadic group (562 words) [view diff] exact match in snippet view article find links to article

The subgroup preserving the Lie bracket (over the integers) is a maximal subgroup of the Thompson group called the Dempwolff group (which unlike the

Conway group (2,300 words) [view diff] exact match in snippet view article find links to article

order of any subgroup of Co0 that properly contains N; hence N is a maximal subgroup of Co0 and contains 2-Sylow subgroups of Co0. N also is the subgroup

Schützenberger group (508 words) [view diff] exact match in snippet view article find links to article

the Schützenberger group associated with the H-class H. If H is a maximal subgroup of a monoid M, then H is an H-class, and it is naturally isomorphic

3D4 (705 words) [view diff] exact match in snippet view article find links to article

automorphism group of order 3. The automorphism group of 3D4(23) is a maximal subgroup of the Thompson sporadic group, and is also a subgroup of the compact

Mathieu group M24 (3,009 words) [view diff] exact match in snippet view article find links to article

extension of M21 by the symmetric group S3. PΓL(3,4) has an embedding as a maximal subgroup of M24.(Griess 1998, p. 55) A hyperoval has no 3 points that are collinear

Robert Arnott Wilson (665 words) [view diff] exact match in snippet view article find links to article

ISBN 9789814486422. with Petra E. Holmes: Holmes, P.E; Wilson, R.A (2002). "A new maximal subgroup of the Monster". Journal of Algebra. 251 (1): 435–447. doi:10.1006/jabr

PSL(2,7) (1,570 words) [view diff] exact match in snippet view article

imaginary quadratic number fields of class number 1. PSL(2, 7) is a maximal subgroup of the Mathieu group M21; the groups M21 and M24 can be constructed

Jan Saxl (741 words) [view diff] exact match in snippet view article find links to article

proof of the O'Nan–Scott theorem. It had long been known that every maximal subgroup of a symmetric group or alternating group was intransitive, imprimitive

Conway group Co3 (1,111 words) [view diff] exact match in snippet view article find links to article

\mathrm {Co} _{3}} as follows: McL:2 – McL fixes a 2-2-3 triangle. The maximal subgroup also includes reflections of the triangle. C o 3 {\displaystyle \mathrm

Mathieu group (2,139 words) [view diff] exact match in snippet view article find links to article

constructed in various ways. M12 has a simple subgroup of order 660, a maximal subgroup. That subgroup is isomorphic to the projective special linear group

Superstring theory (2,978 words) [view diff] exact match in snippet view article find links to article

thought, however, that 16 is probably the maximum since SO(16) is a maximal subgroup of E8, the largest exceptional Lie group, and also is more than large

Green's relations (2,274 words) [view diff] no match in snippet view article find links to article

bold are the idempotents. Any H-class containing one of these is a (maximal) subgroup. In particular, the third D-class is isomorphic to the symmetric group

Semilinear map (2,059 words) [view diff] exact match in snippet view article find links to article

group M24, which is one of the sporadic simple groups; PΓL(3,4) is a maximal subgroup of M24, and there are many ways to extend it to the full Mathieu group

Muller–Schupp theorem (2,037 words) [view diff] exact match in snippet view article find links to article

context-free word problem as being precisely those with a virtually free maximal subgroup. Subsequent to the 1983 paper of Muller and Schupp, several authors

Straight-line program (1,565 words) [view diff] exact match in snippet view article find links to article

following is a straight-line program that computes a generating set for a maximal subgroup E32·E32⋊C31. This straight-line program can be found in the online

Sigma model (4,133 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Phi =G/H} where H ⊂ G {\displaystyle H\subset G} is the maximal subgroup of G {\displaystyle G} that is invariant under the Cartan involution

Automorphisms of the symmetric and alternating groups (3,187 words) [view diff] exact match in snippet view article find links to article

exceptional itself. The full automorphism group of A6 appears naturally as a maximal subgroup of the Mathieu group M12 in 2 ways, as either a subgroup fixing a division

Orthogonal group (7,820 words) [view diff] exact match in snippet view article find links to article

det(A) = 1 is SO(n). A maximal torus in a compact Lie group G is a maximal subgroup among those that are isomorphic to Tk for some k, where T = SO(2) is

Descendant tree (group theory) (7,802 words) [view diff] exact match in snippet view article

possess an abelian maximal subgroup, those with parameter a=1{\displaystyle a=1} do not. More precisely, an existing abelian maximal subgroup is unique, except

Artin transfer (group theory) (26,085 words) [view diff] exact match in snippet view article

cyclic of order p2{\displaystyle p^{2}}. However, for the distinguished maximal subgroup Hp+1{\displaystyle H_{p+1}}, for which the factor group Hp+1/G′{\displaystyle

Symmetric cone (16,607 words) [view diff] exact match in snippet view article find links to article

normal subgroup, then the Bruhat decomposition implies that B is a maximal subgroup, so that either K is contained in B or KB = SL(2,k). In the first case