Baer Lie property is not subgroup-closed

From Groupprops
Revision as of 16:07, 2 July 2017 by Vipul (talk | contribs) (Created page with "{{group metaproperty dissatisfaction| property = Baer Lie group| metaproperty = subgroup-closed group property}} ==Statement== It is possible to have a Baer Lie group (a...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article gives the statement, and possibly proof, of a group property (i.e., Baer Lie group) not satisfying a group metaproperty (i.e., subgroup-closed group property).
View all group metaproperty dissatisfactions | View all group metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for group properties
Get more facts about Baer Lie group|Get more facts about subgroup-closed group property|

Statement

It is possible to have a Baer Lie group (a 2-powered class two group) G and a subgroup H of G that is not a Baer Lie group.

Related facts

Similar facts

Opposite facts

Proof

Further information: unitriangular matrix group:UT(3,Q), unitriangular matrix group:UT(3,Z)

Consider the example G = UT(3,\mathbb{Q}) and H = UT(3,\mathbb{Z}). G is a Baer Lie group. H is a group of class exactly two that is not 2-powered, hence, it is not a Baer Lie group.