Year: 2023
Type: preprint
Abstract: In this work we show that every minimal code in a semisimple group algebra $\mathbb{F}_qG$ is essential if $G$ is a simple group. Since the alternating group $A_n$ is simple if $n=3$ or $n\geq 5$, we present some examples of minimal codes in $\mathbb{F}_qA_n$. For this purpose, if $char(\mathbb{F}_q)> n$, we present the Wedderburn-Artin decomposition of $\mathbb{F}_qS_n$ and $\mathbb{F}_qA_n$ and explicit some of the centrally primitive idempotents of $\mathbb{F}_qS_n$ and $\mathbb{F}_qA_n$.
Source: arXiv (Cornell University)
Institutions: Federal Institute of São Paulo, Universidade de São Paulo
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1664733878, G4402799499, G8727621224
OpenAlex ID: W4387995388