Vipul: New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup $H$ of a group $G$ is termed a '''sub-isomorph-free subgroup''' if there exists an ascending c...

2009-03-06T22:51:23Z

New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup <math>H</math> of a group <math>G</math> is termed a '''sub-isomorph-free subgroup''' if there exists an ascending c...

New page

{{wikilocal}}
{{subgroup property}}

==Definition==

A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed a '''sub-isomorph-free subgroup''' if there exists an ascending chain of subgroups:

<math>H = H_0 \le H_1 \le H_2 \le \dots \le H_n = G</math>

such that each <math>H_i</math> is an [[defining ingredient::isomorph-free subgroup]] of <math>H_{i+1}</math>.

==Effect of property operators==

{{obtainedbyapplyingthe|subordination operator|isomorph-free subgroup}}

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Isomorph-free subgroup]]

===Weaker properties===

* [[Stronger than::Sub-(isomorph-normal characteristic) subgroup]]
* [[Stronger than::Left-transitively WNSCDIN-subgroup]]
* [[Stronger than::Characteristic subgroup]]
* [[Stronger than::Normal subgroup]]

==Metaproperties==

{{transitive}}

Sub-isomorph-free subgroup - Revision history

Vipul: New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup H of a group G is termed a '''sub-isomorph-free subgroup''' if there exists an ascending c...

Vipul: New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup $H$ of a group $G$ is termed a '''sub-isomorph-free subgroup''' if there exists an ascending c...