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Post Closed as "Duplicate" by Ben Webster♦
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T. Amdeberhan
T. Amdeberhan
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It is known that the intersectionnintersection of kernels of all ireductibileireducible representations of a finite group in charcteristiccharacteristic zero is the trivial group.

In caracteristic pcharacteristic $p>0$ I have understood that this intersection îs $O_p(G)$, the largest normal p $p$ - subgroup of G$G$. In other words, all irreducible represntationsrepresentations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proovedifficulties in proving this similar result in characteristic p$p$ dividing the order of G$G$. Could Simeone please givesomeone provide me with a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.

It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero is the trivial group.

In caracteristic p I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could Simeone please give a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.

It is known that the intersection of kernels of all ireducible representations of a finite group in characteristic zero is the trivial group.

In characteristic $p>0$ I have understood that this intersection îs $O_p(G)$, the largest normal $p$ - subgroup of $G$. In other words, all irreducible representations of G are coming from the quotient $G/O_p(G)$.

I have some difficulties in proving this similar result in characteristic $p$ dividing the order of $G$. Could someone provide me with a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.

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edit approved Jan 11, 2017 at 22:07
user103474
edit approved Jan 11, 2017 at 22:07
user103474
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It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero it îsis the trivial group.

In caracteristic Pp I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could Simeone please give a reference for this result? Or shortly explain the argument to me. My intuition îsis that this îsis not so difficult.

It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero it îs trivial.

In caracteristic P I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could please give a reference for this result? Or shortly explain the argument. My intuition îs that this îs not so difficult.

It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero is the trivial group.

In caracteristic p I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could Simeone please give a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.

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mathuser17
mathuser17
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Ireducible representations in characteristic p

It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero it îs trivial.

In caracteristic P I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could please give a reference for this result? Or shortly explain the argument. My intuition îs that this îs not so difficult.