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dward1996
dward1996
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Let K be a finite field and let R,P be groups (with R a subgroup of P). I know that the irreducible KP-modules have dimensions 1,4 and 16 over K. I have a KP-module M, and I know that M has dimension at most 5 over K. I also know that M does not have a quotient of dimension 1 over K. Moreover, if I consider M as a module over KR, it has a 2-dimensional irreducible module. Is it necessarily the case that M is a 4-dimensional irreducible module over KP? (my initial reasoning can be found in a comment below)

Let K be a finite field and let R,P be groups (with R a subgroup of P). I know that the irreducible KP-modules have dimensions 1,4 and 16 over K. I have a KP-module M, and I know that M has dimension at most 5 over K. I also know that M does not have a quotient of dimension 1 over K. Moreover, if I consider M as a module over KR, it has a 2-dimensional irreducible module. Is it necessarily the case that M is a 4-dimensional irreducible module over KP?

Let K be a finite field and let R,P be groups (with R a subgroup of P). I know that the irreducible KP-modules have dimensions 1,4 and 16 over K. I have a KP-module M, and I know that M has dimension at most 5 over K. I also know that M does not have a quotient of dimension 1 over K. Moreover, if I consider M as a module over KR, it has a 2-dimensional irreducible module. Is it necessarily the case that M is a 4-dimensional irreducible module over KP? (my initial reasoning can be found in a comment below)

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dward1996
dward1996
  • 295
  • 3
  • 10

Restrictions of Modules and Dimensions

Let K be a finite field and let R,P be groups (with R a subgroup of P). I know that the irreducible KP-modules have dimensions 1,4 and 16 over K. I have a KP-module M, and I know that M has dimension at most 5 over K. I also know that M does not have a quotient of dimension 1 over K. Moreover, if I consider M as a module over KR, it has a 2-dimensional irreducible module. Is it necessarily the case that M is a 4-dimensional irreducible module over KP?