On the growth sequences of the free products of some copies of PSL(n,q
Year
: 2008
Abstract: Let $G$ be a finitely generated group and $G^n$ be the direct
product of $n$ copies of $G$. The growth sequence of $G$ is the
sequence $\\\\\\\\\\\\\\\\{d(G^n)\\\\\\\\\\\\\\\\}_{n \\\\\\\\\\\\\\\\geq1}$, where $d(G^n)$ is the minimum
number of generators of $G^n$. The purpose of this article is to
investigate the growth sequences of $G$, where $G=\\\\\\\\\\\\\\\\kcopy$ is the
free products of $k$ copies of the projective special linear simple
group $\\\\\\\\\\\\\\\\ps$, $m,q \\\\\\\\\\\\\\\\geq 2$. In fact, we establish that
$d\\\\\\\\\\\\\\\\left(G^{h(2,\\\\\\\\\\\\\\\\ps)^k}\\\\\\\\\\\\\\\\right) = 2k$ for all $m,q \\\\\\\\\\\\\\\\geq 2$, where
$h(2,\\\\\\\\\\\\\\\\ps)$ is the maximum number $t$ such that $d(\\\\\\\\\\\\\\\\ps ^t)=2$.
Moreover, we prove that \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
$d\\\\\\\\\\\\\\\\left(( \\\\\\\\\\\\\\\\mkcopy )^t \\\\\\\\\\\\\\\\right)=2k $ \\\\\\\\\\\\\\\\hspace{0.2 cm} for all $m_i,q_i
\\\\\\\\\\\\\\\\geq 2$, $1 \\\\\\\\\\\\\\\\leq i \\\\\\\\\\\\\\\\leq k$ and \\\\\\\\\\\\\\\\hspace{0.2 cm} $ 1 \\\\\\\\\\\\\\\\leq t \\\\\\\\\\\\\\\\leq
h(2,\\\\\\\\\\\\\\\\pk)h(2,\\\\\\\\\\\\\\\\pkk) \\\\\\\\\\\\\\\\cdots h(2,\\\\\\\\\\\\\\\\pkn)$.\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\noindent We have also
confirmed the above
results by several examples in find section.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
product of $n$ copies of $G$. The growth sequence of $G$ is the
sequence $\\\\\\\\\\\\\\\\{d(G^n)\\\\\\\\\\\\\\\\}_{n \\\\\\\\\\\\\\\\geq1}$, where $d(G^n)$ is the minimum
number of generators of $G^n$. The purpose of this article is to
investigate the growth sequences of $G$, where $G=\\\\\\\\\\\\\\\\kcopy$ is the
free products of $k$ copies of the projective special linear simple
group $\\\\\\\\\\\\\\\\ps$, $m,q \\\\\\\\\\\\\\\\geq 2$. In fact, we establish that
$d\\\\\\\\\\\\\\\\left(G^{h(2,\\\\\\\\\\\\\\\\ps)^k}\\\\\\\\\\\\\\\\right) = 2k$ for all $m,q \\\\\\\\\\\\\\\\geq 2$, where
$h(2,\\\\\\\\\\\\\\\\ps)$ is the maximum number $t$ such that $d(\\\\\\\\\\\\\\\\ps ^t)=2$.
Moreover, we prove that \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
$d\\\\\\\\\\\\\\\\left(( \\\\\\\\\\\\\\\\mkcopy )^t \\\\\\\\\\\\\\\\right)=2k $ \\\\\\\\\\\\\\\\hspace{0.2 cm} for all $m_i,q_i
\\\\\\\\\\\\\\\\geq 2$, $1 \\\\\\\\\\\\\\\\leq i \\\\\\\\\\\\\\\\leq k$ and \\\\\\\\\\\\\\\\hspace{0.2 cm} $ 1 \\\\\\\\\\\\\\\\leq t \\\\\\\\\\\\\\\\leq
h(2,\\\\\\\\\\\\\\\\pk)h(2,\\\\\\\\\\\\\\\\pkk) \\\\\\\\\\\\\\\\cdots h(2,\\\\\\\\\\\\\\\\pkn)$.\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\noindent We have also
confirmed the above
results by several examples in find section.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
Keyword(s): Minimum number of generators,growth sequences,free product,projective linear group
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On the growth sequences of the free products of some copies of PSL(n,q
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| contributor author | احمد عرفانیان مشیری نژاد | en |
| contributor author | Ahmad Erfanian | fa |
| date accessioned | 2020-06-06T13:51:26Z | |
| date available | 2020-06-06T13:51:26Z | |
| date issued | 2008 | |
| identifier uri | http://libsearch.um.ac.ir:80/fum/handle/fum/3372084 | |
| description abstract | Let $G$ be a finitely generated group and $G^n$ be the direct product of $n$ copies of $G$. The growth sequence of $G$ is the sequence $\\\\\\\\\\\\\\\\{d(G^n)\\\\\\\\\\\\\\\\}_{n \\\\\\\\\\\\\\\\geq1}$, where $d(G^n)$ is the minimum number of generators of $G^n$. The purpose of this article is to investigate the growth sequences of $G$, where $G=\\\\\\\\\\\\\\\\kcopy$ is the free products of $k$ copies of the projective special linear simple group $\\\\\\\\\\\\\\\\ps$, $m,q \\\\\\\\\\\\\\\\geq 2$. In fact, we establish that $d\\\\\\\\\\\\\\\\left(G^{h(2,\\\\\\\\\\\\\\\\ps)^k}\\\\\\\\\\\\\\\\right) = 2k$ for all $m,q \\\\\\\\\\\\\\\\geq 2$, where $h(2,\\\\\\\\\\\\\\\\ps)$ is the maximum number $t$ such that $d(\\\\\\\\\\\\\\\\ps ^t)=2$. Moreover, we prove that \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ $d\\\\\\\\\\\\\\\\left(( \\\\\\\\\\\\\\\\mkcopy )^t \\\\\\\\\\\\\\\\right)=2k $ \\\\\\\\\\\\\\\\hspace{0.2 cm} for all $m_i,q_i \\\\\\\\\\\\\\\\geq 2$, $1 \\\\\\\\\\\\\\\\leq i \\\\\\\\\\\\\\\\leq k$ and \\\\\\\\\\\\\\\\hspace{0.2 cm} $ 1 \\\\\\\\\\\\\\\\leq t \\\\\\\\\\\\\\\\leq h(2,\\\\\\\\\\\\\\\\pk)h(2,\\\\\\\\\\\\\\\\pkk) \\\\\\\\\\\\\\\\cdots h(2,\\\\\\\\\\\\\\\\pkn)$.\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\noindent We have also confirmed the above results by several examples in find section.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ | en |
| language | English | |
| title | On the growth sequences of the free products of some copies of PSL(n,q | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | Minimum number of generators | en |
| subject keywords | growth sequences | en |
| subject keywords | free product | en |
| subject keywords | projective linear group | en |
| journal title | International Journal of Mathematics, Game Theory and Algebra | en |
| journal title | International Journal of Mathematics, Game Theory and Algebra | fa |
| pages | 17-Nov | |
| journal volume | 18 | |
| journal issue | 1 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1009473.html | |
| identifier articleid | 1009473 |