𝑝-group
Sign in to saveAlso known as p-primary group, primary group, 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 n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p''.
~13 min read
Article
21 sectionsContents
- Properties
- Non-trivial center
- Automorphisms
- Examples
- Iterated wreath products
- Generalized dihedral groups
- Unitriangular matrix groups
- Classification
- Up to ''p''<sup>3</sup>
- Prevalence
- Among groups
- Within a group
- Application to structure of a group
- Local control
- See also
- Footnotes
- Notes
- Citations
- References
- Further reading
- External links
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 n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p.
Abelian p-groups are also called 'p-primary or simply primary'.