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BHZ
BHZ
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LotLet $p> 3$ be a prime number and $G$ be a finite group of order $p(p^2-1) / 4 $. If $ 4 \mid (p+1)$ then easily we can see that the $ p$ Sylow-Sylow subgroup of $G$ is a normal subgroup of $G$. As I checked it seems that for each $p$ this result holdsgholds i.e. the $ p$ Sylow-Sylow subgroup of $G$ is a normal subgroup of $G$. Any references or hints would be highly appreciated. Thanks in advance.

Lot $p> 3$ be a prime number and $G$ be a finite group of order $p(p^2-1) / 4 $. If $ 4 \mid (p+1)$ then easily we can see that the $ p$ Sylow subgroup of $G$ is a normal subgroup of $G$. As I checked it seems that for each $p$ this result holdsg i.e. the $ p$ Sylow subgroup of $G$ is a normal subgroup of $G$. Any references or hints would be highly appreciated. Thanks in advance.

Let $p> 3$ be a prime number and $G$ be a finite group of order $p(p^2-1) / 4 $. If $ 4 \mid (p+1)$ then easily we can see that the $ p$-Sylow subgroup of $G$ is a normal subgroup of $G$. As I checked it seems that for each $p$ this result holds i.e. the $ p$-Sylow subgroup of $G$ is a normal subgroup of $G$. Any references or hints would be highly appreciated. Thanks in advance.

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BHZ
BHZ
  • 1.2k
  • 5
  • 11

groups of order $ p(p^2-1) / 4 $ where $p$ is a prime

Lot $p> 3$ be a prime number and $G$ be a finite group of order $p(p^2-1) / 4 $. If $ 4 \mid (p+1)$ then easily we can see that the $ p$ Sylow subgroup of $G$ is a normal subgroup of $G$. As I checked it seems that for each $p$ this result holdsg i.e. the $ p$ Sylow subgroup of $G$ is a normal subgroup of $G$. Any references or hints would be highly appreciated. Thanks in advance.