Vipul at 00:44, 2 February 2012

2012-02-02T00:44:32Z

← Older revision		Revision as of 00:44, 2 February 2012
Line 9:		Line 9:
	==Facts==		==Facts==

	* [[Join of all abelian normal subgroups is isoclinism-~~invarant~~]]		* [[Join of all abelian normal subgroups is isoclinism-invariant]]

Vipul: Created page with "{{subgroup-defining function}} ==Definition== Suppose $G$ is a group. The '''join of all abelian normal subgroups''' of $G$ is the subgroup of ..."

2012-02-02T00:44:27Z

Created page with "{{subgroup-defining function}} ==Definition== Suppose <math>G</math> is a group. The '''join of all abelian normal subgroups''' of <math>G</math> is the subgroup of ..."

New page

{{subgroup-defining function}}

==Definition==

Suppose <math>G</math> is a [[group]]. The '''join of all abelian normal subgroups''' of <math>G</math> is the [[subgroup]] of <matH>G</math> defined as the [[join of subgroups|join]] of ''all'' the [[abelian normal subgroup]]s of <math>G</math>.

If <math>G</math> is a [[finite group]] (or more generally a [[group satisfying ascending chain condition on normal subgroups]]) then this is equivalent to the join of all subgroups that are [[maximal among abelian normal subgroups]].

==Facts==

* [[Join of all abelian normal subgroups is isoclinism-invarant]]

Join of all abelian normal subgroups - Revision history

Vipul at 00:44, 2 February 2012

Vipul: Created page with "{{subgroup-defining function}} ==Definition== Suppose G is a group. The '''join of all abelian normal subgroups''' of G is the subgroup of ..."

Vipul: Created page with "{{subgroup-defining function}} ==Definition== Suppose $G$ is a group. The '''join of all abelian normal subgroups''' of $G$ is the subgroup of ..."