Search results

...algebra]] and [[finite geometry]], the '''list of transitive finite linear groups''' is an important classification of certain highly symmetric [[Group actio ...vides a complete <!-- and irredundant? --> list of the finite 2-transitive groups whose socle is [[elementary abelian group|elementary abelian]]. ...

...e algebra of <math>E_{8}</math>, and is also contained in the [[Thompson sporadic group]] (the full automorphism group of this lattice) as a maximal subgroup ...^{4\,.}\mathrm{GL}_{4}(\mathbb{F}_{2})</math> is a maximal subgroup of the sporadic [[Conway group]]&nbsp;Co₃. ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Fischer sporadic groups|Fischer group}} ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Fischer sporadic groups|Fischer group}} ...

{{Short description|Sporadic simple group}} ...n algebra known as [[group theory]], the '''McLaughlin group''' McL is a [[sporadic simple group]] of [[Order (group theory)|order]] ...

| image = ATLAS of Finite Groups cover.jpg | caption = ''ATLAS of Finite Groups'' distinctive cherry red cardboard cover and spiral binding ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Fischer sporadic groups|Fischer group}} ...

...thorlink=Charles Sims (mathematician) |title=Graphs and finite permutation groups |journal=[[Mathematische Zeitschrift]] |volume=95 |number=1 |year=1967 |pag ...in particular the fact that only finitely many [[isomorphism]] types of [[sporadic group]]s exist. ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Conway sporadic groups|Conway group}} ...

...al of the [[sporadic simple group]]s were discovered as rank 3 permutation groups. The primitive rank 3 permutation groups are all in one of the following classes: ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Conway sporadic groups|Conway group}} ...

{{Short description|Sporadic simple group}} {{for|general background and history of the Conway sporadic groups|Conway group}} ...

...lattice, which is a double cover of the [[Conway group]] Co₁, a sporadic simple group. ...[[Neil Sloane|Sloane, N. J. A.]] (1999). ''Sphere packings, lattices and groups.'' (3rd ed.) With additional contributions by E. Bannai, [[Richard Borcher ...

.../212051/Holdings "Classification of RWPRI geometries for the Suzuki simple groups"], PhD Thesis, 1998, Dépôt institutionnel, ''[[Université libre de Bruxelle ...dually Weakly Primitive and Locally Two-transitive Geometries for Sporadic Groups par Dimitri Leemans. Rapports des Commissaires, ...

...e the [[Hall-Janko group]] and the [[Mathieu group]]s, act as automorphism groups of near polygons. |title=The Witt designs, Golay codes and Mathieu groups}}</ref> ...

...oradic groups]] as Galois groups over <math>\Q</math> — the only remaining sporadic group left to realize being the [[Mathieu group M23]]. ...ox |first1=R. |last2=Neuwirth |first2=L. |date=1962-06-01 |title=The Braid Groups. |journal=Mathematica Scandinavica |url=http://www.mscand.dk/article/view/1 ...

...'' ≥ 4}}, the covering groups are 2-fold covers except for the alternating groups of degree 6 and 7 where the covers are 6-fold. The Schur covers of the symmetric and alternating groups were classified in {{harv|Schur|1911}}. The symmetric group of degree {{no ...

...ique, there are exactly two semilinear extensions; for example, symplectic groups have a unique semilinear extension, while {{nowrap|SU(''n'', ''q'')}} has t ...author=Ian R. Porteous|year=1995|title=Clifford Algebras and the Classical Groups|publisher=[[Cambridge University Press]]}}}}{{refn|{{citation|author=Bourba ...

...e (graph theory)|descendant tree]] are isomorphism classes of finite ''p''-groups. ...endant trees play a fundamental role in the classification of finite ''p''-groups. By means of kernels and targets of [[Artin transfer (group theory)#Structu ...

...s]] <math>U_q(\mathfrak{g})^+</math> of the infinite-dimensional [[quantum groups]] when ''q'' is no root of unity, and the first examples of finite-dimensio ...tor space <math>V</math> and can therefore be realized over many different groups. Sometimes there are two or three Nichols algebras with different <math>V</ ...