mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

p-group In mathematics, specifically group theory, given a prime number ''p'', a ''p''-group is a group in which the order of every element is a power of ''p''. That is, for each element ''g'' of a ''p''-group ''G'', there exists a nonnegative integer ...

G

is called power closed if for every section

H

G

the product of

p^k

powers is again a

p^k

th 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^k

th 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 .

References

* Group theory P-groups {{group-theory-stub