Difference between revisions of "Rationally powered group of nilpotency class two"

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{{group property conjunction|rationally powered group|group of nilpotency class two}}
 
{{group property conjunction|rationally powered group|group of nilpotency class two}}
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==Definition==
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A [[group]] <math>G</math> is termed a '''rationally powered class two group''' or a '''rationally powered group of nilpotency class two''' if <math>G</math> is a [[rationally powered group]] (i.e., it is [[powered group for a set of primes|powered over]] all primes) as well as a [[group of nilpotency class two]].
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==Relation with other properties==
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===Weaker properties===
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{| class="sortable" border="1"
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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
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|-
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| [[Stronger than::rationally powered nilpotent group]] || || || || {{intermediate notions short|rationally powered nilpotent group|rationally powered group of nilpotency class two}}
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|-
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| [[Stronger than::gradable nilpotent group]] || || || || {{intermediate notions short|gradable nilpotent group|rationally powered group of nilpotency class two}}
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|}

Latest revision as of 20:53, 11 August 2013

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: rationally powered group and group of nilpotency class two
View other group property conjunctions OR view all group properties

Definition

A group G is termed a rationally powered class two group or a rationally powered group of nilpotency class two if G is a rationally powered group (i.e., it is powered over all primes) as well as a group of nilpotency class two.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
rationally powered nilpotent group |FULL LIST, MORE INFO
gradable nilpotent group |FULL LIST, MORE INFO