Exterior square of finite group is finite - Revision history

Vipul at 17:06, 29 June 2013

2013-06-29T17:06:05Z

← Older revision		Revision as of 17:06, 29 June 2013
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	Suppose <math>G</math> is a [[finite group]]. Then, the [[fact about::exterior square of a group;2\| ]][[exterior square]] of <math>G</math> is also a [[finite group]].		Suppose <math>G</math> is a [[finite group]]. Then, the [[fact about::exterior square of a group;2\| ]][[exterior square]] of <math>G</math> is also a [[finite group]].

			==Applications==

			* [[Schur-Baer theorem]]: This states that if the [[inner automorphism group]] of a group is finite, so is the [[derived subgroup]] of the group.

	==Facts used==		==Facts used==

Vipul at 21:07, 20 January 2013

2013-01-20T21:07:27Z

← Older revision		Revision as of 21:07, 20 January 2013
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	==Statement==		==Statement==

	Suppose <math>G</math> is a [[finite group]]. Then, the [[exterior square]] of <math>G</math> is also a [[finite group]].		Suppose <math>G</math> is a [[finite group]]. Then, the [[fact about::exterior square of a group;2\| ]][[exterior square]] of <math>G</math> is also a [[finite group]].

	==Facts used==		==Facts used==

Vipul: Created page with "==Statement== Suppose $G$ is a finite group. Then, the exterior square of $G$ is also a finite group. ==Facts used== # uses::Commutator ..."

2013-01-20T21:07:09Z

Created page with "==Statement== Suppose <math>G</math> is a finite group. Then, the exterior square of <math>G</math> is also a finite group. ==Facts used== # uses::Commutator ..."

New page

==Statement==

Suppose <math>G</math> is a [[finite group]]. Then, the [[exterior square]] of <math>G</math> is also a [[finite group]].

==Facts used==

# [[uses::Commutator map is homomorphism from exterior square to derived subgroup]], and the kernel of this homomorphism is the [[Schur multiplier]].
# [[uses::Schur multiplier of finite group is finite]]

==Proof==

The proof basically follows directly by combining Facts (1) and (2).

Exterior square of finite group is finite - Revision history

Vipul at 17:06, 29 June 2013

Vipul at 21:07, 20 January 2013

Vipul: Created page with "==Statement== Suppose G is a finite group. Then, the exterior square of G is also a finite group. ==Facts used== # uses::Commutator ..."

Vipul: Created page with "==Statement== Suppose $G$ is a finite group. Then, the exterior square of $G$ is also a finite group. ==Facts used== # uses::Commutator ..."