Permutable implies locally subnormal - Revision history

Vipul at 22:24, 31 March 2009

2009-03-31T22:24:25Z

← Older revision		Revision as of 22:24, 31 March 2009
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	Any [[permutable subgroup]] of a [[group]] is a [[locally subnormal subgroup]] -- it is subnormal in its join with any finitely generated subgroup.		Any [[permutable subgroup]] of a [[group]] is a [[locally subnormal subgroup]] -- it is subnormal in its join with any finitely generated subgroup.

			==Related facts==

			* [[Permutable implies subnormal in finite]]
			* [[Permutable implies ascendant]]

	==References==		==References==

Vipul at 22:22, 31 March 2009

2009-03-31T22:22:00Z

← Older revision		Revision as of 22:22, 31 March 2009
Line 6:		Line 6:

	Any [[permutable subgroup]] of a [[group]] is a [[locally subnormal subgroup]] -- it is subnormal in its join with any finitely generated subgroup.		Any [[permutable subgroup]] of a [[group]] is a [[locally subnormal subgroup]] -- it is subnormal in its join with any finitely generated subgroup.

			==References==

			===Textbook references===

			* {{booklink-proved\|LennoxStonehewer\|216\|Theorem 7.1.8}}

Vipul: Created page with '{{subgroup property implication| stronger = permutable subgroup| weaker = locally subnormal subgroup}} ==Statement== Any permutable subgroup of a group is a [[locally s...'

2009-03-31T22:19:06Z

Created page with '{{subgroup property implication| stronger = permutable subgroup| weaker = locally subnormal subgroup}} ==Statement== Any permutable subgroup of a group is a [[locally s...'

New page

{{subgroup property implication|
stronger = permutable subgroup|
weaker = locally subnormal subgroup}}

==Statement==

Any [[permutable subgroup]] of a [[group]] is a [[locally subnormal subgroup]] -- it is subnormal in its join with any finitely generated subgroup.