# Searching for fractal structures in the Universal Steenrod Algebra at odd primes

## TL;DR

This paper investigates the structure of the universal Steenrod Algebra at odd primes, revealing nested subalgebras that resemble initial elements, despite the absence of a fractal structure seen at p=2.

## Contribution

It identifies and characterizes two distinct families of nested subalgebras within Q(p) at odd primes, highlighting structural differences from the p=2 case.

## Key findings

- No fractal structure preserving monomial length at odd primes
- Existence of two families of nested subalgebras in Q(p)
- Subalgebras are isomorphic to initial elements of the sequence

## Abstract

Unlike the p = 2 case, the universal Steenrod Algebra Q(p) at odd primes does not have a fractal structure that preserves the length of monomials. Nevertheless, when p is odd we detect inside Q(p) two different families of nested subalgebras each isomorphic (as length-graded algebras) to the respective starting element of the sequence