A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$
Let $G=SL_2(p^f)$ 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 a...
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University of Isfahan
2014-12-01
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| Series: | International Journal of Group Theory |
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| Online Access: | http://www.theoryofgroups.ir/pdf_4976_a69c9b523546d6cc0812f1d9027240e7.html |
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doaj-14d8e6fb3b4a4440a6ebf1eface4a6a12020-11-24T22:26:32ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692014-12-01343336A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$Jiangtao Shi 0Yantai UniversityLet $G=SL_2(p^f)$ 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 $p^{2f}equiv 1,(mod 16)$.http://www.theoryofgroups.ir/pdf_4976_a69c9b523546d6cc0812f1d9027240e7.htmlspecial linear groupSylow subgroupnormalizernilpotentsupersolvable |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jiangtao Shi |
| spellingShingle |
Jiangtao Shi A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ International Journal of Group Theory special linear group Sylow subgroup normalizer nilpotent supersolvable |
| author_facet |
Jiangtao Shi |
| author_sort |
Jiangtao Shi |
| title |
A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ |
| title_short |
A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ |
| title_full |
A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ |
| title_fullStr |
A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ |
| title_full_unstemmed |
A note on the normalizer of Sylow 2-subgroup of special linear group $SL_2(p^f)$ |
| title_sort |
note on the normalizer of sylow 2-subgroup of special linear group $sl_2(p^f)$ |
| publisher |
University of Isfahan |
| series |
International Journal of Group Theory |
| issn |
2251-7650 2251-7669 |
| publishDate |
2014-12-01 |
| description |
Let $G=SL_2(p^f)$ 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 $p^{2f}equiv 1,(mod 16)$. |
| topic |
special linear group Sylow subgroup normalizer nilpotent supersolvable |
| url |
http://www.theoryofgroups.ir/pdf_4976_a69c9b523546d6cc0812f1d9027240e7.html |
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AT jiangtaoshi anoteonthenormalizerofsylow2subgroupofspeciallineargroupsl2pf AT jiangtaoshi noteonthenormalizerofsylow2subgroupofspeciallineargroupsl2pf |
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1725753155859251200 |