UCS-Baer Lie group
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Finite UCS-Baer Lie groups coincide with finite Baer Lie groups, and therefore with odd-order class two groups.
In the finite case, UCS-Baer Lie groups coincide with finite Baer Lie groups, and therefore with odd-order class two groups.
An example is central product of UT(3,Z) and Q.
More generally, for a finitely generated torsion-free nilpotent group of class two, we can construct an example by taking the central product of that group with the vector space over the rationals obtained by taking the center. To be more precise, we do not need to use the whole field of rationals: taking the tensor product with should suffice.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Baer Lie group||follows from center is local powering-invariant||central product of UT(3,Z) and Q|||FULL LIST, MORE INFO|
|Property||Meaning||Proof that UCS-Baer Lie group may not have this property||Proof that a group with this property may not be a UCS-Baer Lie group|
|LCS-Baer Lie group||derived subgroup is 2-powered||central product of UT(3,Z) and Q||any abelian group with 2-torsion, such as cyclic group:Z2|