Difference between revisions of "Subgroup of double coset index two"

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==Relation with other properties==
 
==Relation with other properties==
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===Stronger properties===
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* [[Weaker than::Subgroup of index two]]
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* Non-normal subgroup of index three: {{proofat|Index three implies normal or double coset index two]]}}
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* Subgroup of index four that is not [[2-subnormal subgroup|2-subnormal]]: {{proofat|[[Index four implies 2-subnormal or double coset index two]]}}
  
 
===Weaker properties===
 
===Weaker properties===
  
* [[Double coset-separated subgroup]]
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* [[Stronger than::Double coset-separated subgroup]]
* [[Double coset-ordering subgroup]]
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* [[Stronger than::Double coset-ordering subgroup]]
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* [[Stronger than::Maximal subgroup]]: {{proofofstrictimplicationat|[[Double coset index two implies maximal]]|[[Maximal not implies double coset index two]]}}
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* [[Stronger than::1-completed subgroup]]
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* [[Stronger than::Subgroup of finite double coset index]]
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* [[Stronger than::Elliptic subgroup]]

Revision as of 15:47, 31 October 2008

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup is said to have double coset index two if its double coset index is exactly two.

Relation with other properties

Stronger properties

Weaker properties