Validity of a result from character theory for finite field.
Corollary $11.29$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:
Corollary $11.29:$ Let $H$ be a normal subgroup of $G$ and $zetain Irr(G), xiin Irr(H)$, be a constituent of $zeta_{H}$. Then $zeta(1)/ xi(1)$ divides $|G:H|.$
My question is can i say that above corollary is valid over any field or only for $C?$ Please suggest. Thanks.
representation-theory characters
asked 2 days ago
neelkanth
2,0742927
add a comment |
Corollary $11.29$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:
Corollary $11.29:$ Let $H$ be a normal subgroup of $G$ and $zetain Irr(G), xiin Irr(H)$, be a constituent of $zeta_{H}$. Then $zeta(1)/ xi(1)$ divides $|G:H|.$
My question is can i say that above corollary is valid over any field or only for $C?$ Please suggest. Thanks.
representation-theory characters
asked 2 days ago
neelkanth
2,0742927
sorry i will edit...
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
It is given in book ...
– neelkanth
yesterday
add a comment |
Corollary $11.29$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:
Corollary $11.29:$ Let $H$ be a normal subgroup of $G$ and $zetain Irr(G), xiin Irr(H)$, be a constituent of $zeta_{H}$. Then $zeta(1)/ xi(1)$ divides $|G:H|.$
My question is can i say that above corollary is valid over any field or only for $C?$ Please suggest. Thanks.
representation-theory characters
asked 2 days ago
neelkanth
2,0742927
Corollary $11.29$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:
Corollary $11.29:$ Let $H$ be a normal subgroup of $G$ and $zetain Irr(G), xiin Irr(H)$, be a constituent of $zeta_{H}$. Then $zeta(1)/ xi(1)$ divides $|G:H|.$
My question is can i say that above corollary is valid over any field or only for $C?$ Please suggest. Thanks.
representation-theory characters
representation-theory characters
asked 2 days ago
neelkanth
2,0742927
asked 2 days ago
neelkanth
2,0742927
edited 2 days ago
asked 2 days ago
neelkanth
2,0742927
asked 2 days ago
neelkanth
2,0742927
asked 2 days ago
neelkanth
2,0742927
2,0742927
sorry i will edit...
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
It is given in book ...
– neelkanth
yesterday
add a comment |
sorry i will edit...
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
It is given in book ...
– neelkanth
yesterday
sorry i will edit...
– neelkanth
2 days ago
sorry i will edit...
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
It is given in book ...
– neelkanth
yesterday
It is given in book ...
– neelkanth
yesterday
add a comment |
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sorry i will edit...
– neelkanth
2 days ago
@MatthewTowers i edit it.....
– neelkanth
2 days ago
What is your proof for $mathbb{C}$ ?
– reuns
yesterday
It is given in book ...
– neelkanth
yesterday