نتایج جستجو برای: special linear group
تعداد نتایج: 1651799 فیلتر نتایج به سال:
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let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow $2$-subgroup of $g$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. by $n_g(p)$ we denote the normalizer of $p$ in $g$. in this paper, we show that $n_g(p)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}equiv 1,({rm mod},16)$.
let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow $2$-subgroup of $g$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. by $n_g(p)$ we denote the normalizer of $p$ in $g$. in this paper, we show that $n_g(p)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}equiv 1,({rm mod},16)$.
a normal subgroup $n$ of a group $g$ is said to be an $emph{omissible}$ subgroup of $g$ if it has the following property: whenever $xleq g$ is such that $g=xn$, then $g=x$. in this note we construct various groups $g$, each of which has an omissible subgroup $nneq 1$ such that $g/ncong sl_2(k)$ where $k$ is a field of positive characteristic.
let $g$ be a group and $pi(g)$ be the set of primes $p$ such that $g$ contains an element of order $p$. let $nse(g)$ be the set of the number of elements of the same order in $g$. in this paper, we prove that the simple group $l_2(p^2)$ is uniquely determined by $nse(l_2(p^2))$, where $pin{11,13}$.
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