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Deleted space in "$p$-groups"
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Dave Benson
Dave Benson
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I am searching a simple example of a finite group $G$, so that the Jacobson radical $J(FG)$, of group algebra $FG$ is commutative, where $F$ is a finite field. I know example for that if $G$ is any finite abelian group, or dihedral group when characteristic of field is $2$ and $p$- groupsgroups, or when group ring is semi simple. Please provide me any other example of such finite group $G$ for which corresponding Jacobson radical is commutative. Thank you.

I am searching a simple example of a finite group $G$, so that the Jacobson radical $J(FG)$, of group algebra $FG$ is commutative, where $F$ is a finite field. I know example for that if $G$ is any finite abelian group, or dihedral group when characteristic of field is $2$ and $p$- groups, or when group ring is semi simple. Please provide me any other example of such finite group $G$ for which corresponding Jacobson radical is commutative. Thank you.

I am searching a simple example of a finite group $G$, so that the Jacobson radical $J(FG)$, of group algebra $FG$ is commutative, where $F$ is a finite field. I know example for that if $G$ is any finite abelian group, or dihedral group when characteristic of field is $2$ and $p$-groups, or when group ring is semi simple. Please provide me any other example of such finite group $G$ for which corresponding Jacobson radical is commutative. Thank you.

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neelkanth
neelkanth
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Example of a group algebra with commutative Jacobson radical

I am searching a simple example of a finite group $G$, so that the Jacobson radical $J(FG)$, of group algebra $FG$ is commutative, where $F$ is a finite field. I know example for that if $G$ is any finite abelian group, or dihedral group when characteristic of field is $2$ and $p$- groups, or when group ring is semi simple. Please provide me any other example of such finite group $G$ for which corresponding Jacobson radical is commutative. Thank you.