On the growth sequences of the free products of some copies of PSL(n,q

نویسنده:
,
سال
: 2008
چکیده: 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.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
کلیدواژه(گان): Minimum number of generators,growth sequences,free product,projective linear group
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