Power closed

Power closed

In mathematics a p-group G is called power closed if for every section H of G the product of p^k powers is again a p^kth power.

Regular p-groups are an example of power closed groups. On the other hand powerful p-groups, for which the product of p^k powers is again a p^kth power are not power closed, as this property does not hold for all sections of powerful p-groups.

The power closed 2-groups of exponent at least eight are described in harv|Mann|2005|loc=Th. 16.

References

*Citation | last1=Mann | first1=Avinoam | title=The number of generators of finite p-groups | id=MathSciNet | id = 2137973 | year=2005 | journal=Journal of Group Theory | issn=1433-5883 | volume=8 | issue=3 | pages=317–337


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