P-groups

the theorem that, for a finite group of order a mutiple of 𝑝ⁿ, there exist Sylow 𝑝-subgroups of order 𝑝ⁿ (all of whom are conjugate), whose number equals the index of the normalizer of any such subgroup

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''.

mathematical term

commutative group in which all nonzero elements have the same order

infinite group whose proper nontrivial subgroup are all cyclic groups, whose orders all equal a fixed prime number