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''.
Wikidata facts
- Subclass of
- torsion group
Show 2 more facts
- different from
- Sylow subgroup
- maintained by WikiProject
- WikiProject Mathematics
Sources (3)
via Wikidata · CC0
~13 min read
Encyclopedic overview
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'.
Excerpted from Wikipedia’s “𝑝-group” article, available under the CC BY-SA 4.0 licence.