Semi direct product of Quaternion group with cyclic group of order p.
$begingroup$
I am interested in knowing the semi-direct product of Quaternion group $Q_8$ with $c_p$, i.e. cyclic group of order $p$ where $p$ is a odd prime.
We know that $text{SL}_{2}(mathbb{Z}_{3})$ is a semi-direct product of $Q_8$ and $C_3$ from here. Semi-direct products.
Can we generalize above result to $c_p$ for odd prime $p$. Please help.
abstract-algebra finite-groups cyclic-groups semidirect-product
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
$endgroup$
add a comment |
$begingroup$
I am interested in knowing the semi-direct product of Quaternion group $Q_8$ with $c_p$, i.e. cyclic group of order $p$ where $p$ is a odd prime.
We know that $text{SL}_{2}(mathbb{Z}_{3})$ is a semi-direct product of $Q_8$ and $C_3$ from here. Semi-direct products.
Can we generalize above result to $c_p$ for odd prime $p$. Please help.
abstract-algebra finite-groups cyclic-groups semidirect-product
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
$endgroup$
add a comment |
$begingroup$
I am interested in knowing the semi-direct product of Quaternion group $Q_8$ with $c_p$, i.e. cyclic group of order $p$ where $p$ is a odd prime.
We know that $text{SL}_{2}(mathbb{Z}_{3})$ is a semi-direct product of $Q_8$ and $C_3$ from here. Semi-direct products.
Can we generalize above result to $c_p$ for odd prime $p$. Please help.
abstract-algebra finite-groups cyclic-groups semidirect-product
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
$endgroup$
I am interested in knowing the semi-direct product of Quaternion group $Q_8$ with $c_p$, i.e. cyclic group of order $p$ where $p$ is a odd prime.
We know that $text{SL}_{2}(mathbb{Z}_{3})$ is a semi-direct product of $Q_8$ and $C_3$ from here. Semi-direct products.
Can we generalize above result to $c_p$ for odd prime $p$. Please help.
abstract-algebra finite-groups cyclic-groups semidirect-product
abstract-algebra finite-groups cyclic-groups semidirect-product
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
asked Dec 3 '18 at 14:30
Mittal GMittal G
1,243516
1,243516
add a comment |
add a comment |
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