Vipul: New page: {{wikilocal}} {{subofsubgroup property}} ==Definition== Suppose $H \le K \le G$ are groups. We say that $H$ is '''conjugacy-determined''' in $K$ rela...

2008-09-25T12:37:06Z

New page: {{wikilocal}} {{subofsubgroup property}} ==Definition== Suppose <math>H \le K \le G</math> are groups. We say that <math>H</math> is '''conjugacy-determined''' in <math>K</math> rela...

New page

{{wikilocal}}
{{subofsubgroup property}}

==Definition==

Suppose <math>H \le K \le G</math> are [[group]]s. We say that <math>H</math> is '''conjugacy-determined''' in <math>K</math> relative to <math>G</math>, or that <math>K</math> contains fusion of elements of <math>H</math> in <math>G</math>, if two elements of <math>H</math> are conjugate in <math>K</math> if and only if they are conjugate in <math>G</math>.

If <math>H</math> is conjugacy-determined in itself relative to <math>G</math>, <math>H</math> is termed a [[conjugacy-closed subgroup]] of <math>G</math>.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Subset-conjugacy-determined subgroup]]

Conjugacy-determined subgroup - Revision history

Vipul: New page: {{wikilocal}} {{subofsubgroup property}} ==Definition== Suppose H \le K \le G are groups. We say that H is '''conjugacy-determined''' in K rela...

Vipul: New page: {{wikilocal}} {{subofsubgroup property}} ==Definition== Suppose $H \le K \le G$ are groups. We say that $H$ is '''conjugacy-determined''' in $K$ rela...