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On Codes in (Generalized) Symmetric Groups
Abstract
In this article, we show that, for the symmetric group Sn, the Young subgroup Sλ, with l(λ)≥ 3, is not a code with respect to a conjugacy class of Sn. This provides a partial answer to \cite[Problem 4.1]{FL26}. We then provide a characterization of conjugacy classes Xi, such that subgroups S(n−2,1,1), S(n−3,2,1), and Yk for k≤ 3 are codes for X1 ∪ X2. Furthermore, we describe some codes in the finite Coxeter groups of type Bn, Cn, Dn, and in the generalized symmetric group Cm wr Sn.
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BibTeX
@misc{barman2026codes,
title = {{On Codes in (Generalized) Symmetric Groups}},
author = {Subrata Barman and Pushpendra Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21928},
eprint = {2606.21928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21928},
}
RIS
TY - UNPB
TI - On Codes in (Generalized) Symmetric Groups
AU - Subrata Barman
AU - Pushpendra Singh
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2606.21928
UR - https://arxiv.org/abs/2606.21928
AB - In this article, we show that, for the symmetric group S_n, the Young subgroup S_λ, with l(λ)≥ 3, is not a code with respect to a conjugacy class of S_n. This provides a partial answer to \cite[Problem 4.1]{FL26}. We then provide a characterization of conjugacy classes X_i, such that subgroups S_(n−2,1,1), S_(n−3,2,1), and Y_k for k≤ 3 are codes for X_1 ∪ X_2. Furthermore, we describe some codes in the finite Coxeter groups of type B_n, C_n, D_n, and in the generalized symmetric group C_m wr S_n.
ER -