Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometries between finite groups   We prove that if $H$ is a subgroup of index $n$ of any cyclic group $G$, then
$G$ can be isometrically embedded in $(H^n, d_{_{Ham}}^n)$, thus generalizing
previous results of Carlet (1998) for $G=\mathbb{Z}_{2^k}$ and Yildiz-\"Ozger
(2012) for $G=\mathbb{Z}_{p^k}$ with $p$ prime. Next, for any positive integer
$q$ we define the $q$-adic metric $d_q$ in $\mathbb{Z}_{q^n}$ and prove that
$(\mathbb{Z}_{q^n}, d_q)$ is isometric to $(\mathbb{Z}_q^n, d_{RT})$ for every
$n$, where $d_{RT}$ is the Rosenbloom-Tsfasman metric. More generally, we then
demonstrate that any pair of finite groups of the same cardinality are
isometric to each other for some metrics that can be explicitly constructed.
Finally, we consider a chain $\mathcal{C}$ of subgroups of a given group and
define the chain metric $d_{\mathcal{C}}$ and chain isometries between two
chains. Let $G, K$ be groups with $|G|=q^n$, $|K|=q$ and let $H<G$. Using
chains, we prove that under certain conditions, $(G,d_\mathcal{C}) \simeq (K^n,
d_{RT})$ and $(G,d_\mathcal{C}) \simeq (H^{[G:H]}, d_{BRT})$ where $d_{BRT}$ is
the block Rosenbloom-Tsfasman metric which generalizes $d_{RT}$.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio