2-powered group: Difference between revisions

Revision as of 15:59, 5 August 2013

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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Definition

A group is termed a 2-powered group if it is powered over the prime 2, i.e., the square map is bijective from the group to itself, or equivalently, every element has a unique square root. Equivalently, the group is powered over the ring $\mathbb {Z} [1/2]$ .

Relation with other properties

Conjunction with other properties

Conjunction	Other component of conjunction	Intermediate notions
odd-order group	finite group	\|FULL LIST, MORE INFO
Baer Lie group	group of nilpotency class two	\|FULL LIST, MORE INFO

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 ==Definition==
-A [[group]] is termed a '''2-powered group''' if it is [[powered group for a set of primes|powered over]] the prime 2, i.e., the [[square map]] is bijective from the group to itself, or equivalently, every element has a unique square root.
+A [[group]] is termed a '''2-powered group''' if it is [[powered group for a set of primes|powered over]] the prime 2, i.e., the [[square map]] is bijective from the group to itself, or equivalently, every element has a unique square root. Equivalently, the group is [[group powered over a unital ring|powered over]] the ring <math>\mathbb{Z}[1/2]</math>.
 ==Relation with other properties==