Difference between revisions of "D8 in S4"

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(Created page with "{{particular subgroup| group = symmetric group:S4| subgroup = dihedral group:D8}} This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</m...")
 
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This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</math> is [[symmetric group:S4]], i.e., the symmetric group on the set <math>\{ 1,2,3,4 \}</math>, and <math>H</math> is the subgroup:
 
This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</math> is [[symmetric group:S4]], i.e., the symmetric group on the set <math>\{ 1,2,3,4 \}</math>, and <math>H</math> is the subgroup:
  
<math>\! \{ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1,2)(3,4), (1,4)(2,3), (1,3), (2,4) \}</math>
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<math>\! H = \{ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1,2)(3,4), (1,4)(2,3), (1,3), (2,4) \}</math>
  
 
<math>H</math> is a 2-[[Sylow subgroup]] of <math>G</math>, and has two other [[conjugate subgroups]], which are given below:
 
<math>H</math> is a 2-[[Sylow subgroup]] of <math>G</math>, and has two other [[conjugate subgroups]], which are given below:

Revision as of 03:40, 17 December 2010

This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) dihedral group:D8 and the group is (up to isomorphism) symmetric group:S4 (see subgroup structure of symmetric group:S4).
VIEW: Group-subgroup pairs with the same subgroup part | Group-subgroup pairs with the same group part | All pages on particular subgroups in groups

This article is about the subgroup H in the group G, where G is symmetric group:S4, i.e., the symmetric group on the set \{ 1,2,3,4 \}, and H is the subgroup:

\! H = \{ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1,2)(3,4), (1,4)(2,3), (1,3), (2,4) \}

H is a 2-Sylow subgroup of G, and has two other conjugate subgroups, which are given below:

\! H_1 = \{ (), (1,3,2,4), (1,2)(3,4), (1,4,2,3), (1,3)(2,4), (1,4)(2,3), (1,2), (3,4) \}

and:

\! H_2 = \{ (), (1,2,4,3), (1,4)(2,3), (1,3,4,2), (1,2)(3,4), (1,3)(2,4), (1,4), (2,3) \}