# Difference between revisions of "Schur multiplier of cyclic group is trivial"

From Groupprops

m (Vipul moved page Cyclic implies Schur-trivial to Schur multiplier of cyclic group is trivial) |
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+ | {{group property implication| | ||

+ | stronger = cyclic group| | ||

+ | weaker = Schur-trivial group}} | ||

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==Statement== | ==Statement== | ||

Any [[cyclic group]] is a [[Schur-trivial group]]: its [[Schur multiplier]] is the [[trivial group]]. | Any [[cyclic group]] is a [[Schur-trivial group]]: its [[Schur multiplier]] is the [[trivial group]]. |

## Latest revision as of 02:59, 10 January 2013

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., cyclic group) must also satisfy the second group property (i.e., Schur-trivial group)

View all group property implications | View all group property non-implications

Get more facts about cyclic group|Get more facts about Schur-trivial group

## Statement

Any cyclic group is a Schur-trivial group: its Schur multiplier is the trivial group.