# Search results

• {{natural number-parametrized group family}} ...lled [[von Dyck group]]s. They also arise as a special case of a family of groups called [[Coxeter group]]s.
10 KB (1,448 words) - 02:22, 6 July 2019
• ...group}} of order eight or ''the dihedral group of degree four'' (since its natural action is on four elements), or sometimes the ''octic group'', is defined b ...er [[field:F2]], [itex]2[/itex]-[[Sylow subgroup]] of [[projective special linear group:PSL(3,2)|PSL(3,2)]].
19 KB (2,660 words) - 13:15, 14 February 2015
• {{natural number-parametrized linear algebraic group}} ...th>n[/itex] be a natural number and [itex]k[/itex] a field. The '''general linear group''' of degree [itex]n[/itex] over [itex]k[/itex], denoted [itex]GL(n,k
7 KB (1,099 words) - 19:54, 7 July 2019
• {{natural number-parametrized algebraic matrix group}} Let [itex]n[/itex] be a natural number and [itex]k[/itex] be a field. The '''orthogonal group for the stand
6 KB (889 words) - 22:43, 26 February 2010
• {{natural number-parametrized linear algebraic group}} Let [itex]k[/itex] be a [[field]] and [itex]n[/itex] a natural number. The '''orthogonal similitude group for the standard dot product '''
3 KB (392 words) - 18:57, 26 February 2010
• {{natural number-parametrized linear algebraic group}} ===In terms of natural numbers===
5 KB (791 words) - 01:56, 11 February 2010
• {{natural number-parametrized linear algebraic group}} Let [itex]n[/itex] be a natural number and [itex]k[/itex] a field. Then the special orthogonal group of ord
2 KB (255 words) - 23:48, 25 February 2010
• ...tion: given a conjecture stating that something is true for ''all'' finite groups, how do we go about verifying, proving, or disproving the conjecture? A conjecture related to finite groups typically has either of these formats:
6 KB (883 words) - 00:34, 8 May 2008
• {{natural number-parametrized linear algebraic group}} Let [itex]k[/itex] be a field and [itex]n[/itex] be a natural number. The '''special orthogonal similitude group''' of order [itex]n</mat
1 KB (178 words) - 15:16, 16 March 2009
• {{natural number-parametrized linear algebraic group}} Let [itex]k[/itex] be a [[field]] and [itex]n[/itex] be a [[natural number]]. The '''affine orthogonal group''' [itex]AO(n,k)[/itex] is defined
2 KB (376 words) - 14:56, 6 August 2009
• ...ecial linear group over reals]] and hence of a [[member of family::special linear group]]. ...has the structure of a [[topological group]], a [[real Lie group]], and an algebraic group restricted to the reals.
4 KB (568 words) - 19:24, 18 September 2012
• ...ng one block into the Young diagram of the partition of [itex]n[/itex]. In algebraic terms, this means that the partition of [itex]n + 1[/itex] is obtained from ...aph''' is the [[Bratteli diagram]] for the inductive sequence of symmetric groups [itex]S_1 \hookrightarrow S_2 \hookrightarrow S_3 \hookrightarrow \dots \ho
3 KB (533 words) - 15:29, 27 May 2011
• ...ince it belongs to the family of [[standard representation]]s of symmetric groups. | Kernel of representation || trivial subgroup, i.e., it is a [[faithful linear representation]] in all characteristics.
14 KB (1,983 words) - 05:50, 7 June 2012
• ...ince it belongs to the family of [[standard representation]]s of symmetric groups. | Kernel of representation || trivial subgroup, i.e., it is a [[faithful linear representation]] in all characteristics.
14 KB (1,994 words) - 21:43, 17 July 2011
• ...fact about::algebraic group;2| ]][[algebraic group]]s of [[dimension of an algebraic group|dimension]] equal to 1 over an [[fact about::algebraically closed fie ...for the case of a [[linear algebraic group]] (or equivalently, an [[affine algebraic group]]), case (3) does not apply and thus cases (1) and (2) are the only p
4 KB (587 words) - 18:10, 7 January 2012
• ...algebraic group]] over the [[field of real numbers]] (note that it is not algebraic over the complex numbers). ! Function !! Value !! Similar groups !! Explanation
4 KB (623 words) - 07:12, 12 February 2013