N-central group: Difference between revisions

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==Facts==
==Facts==


* If <math>n</math> is an odd prime number <math>p</math>, then <math>n</math>-central implies <math>n</math>-abelian: see [[Frattini-in-center odd-order p-group implies p-power map is endomorphism]]
* [[Frattini-in-center odd-order p-group implies p-power map is endomorphism]]
* [[n-abelian implies n(n-1)-central]]
* [[n-abelian implies n(n-1)-central]]

Latest revision as of 22:55, 7 August 2012

This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

Definition

Suppose is a group and is an integer other than 0. We say that is -central if the exponent of the inner automorphism group of divides .

Note that this is distinct from the notion of p-central group.

Facts