Construction of Groups with favourable character degrees

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In trying to eliminate some graphs associated with character degrees of finite groups, one comes across a challenge of not having enough tools to do the same. This raises a question on whether one can construct a group with favourable outcome. For example:



Suppose I need to construct a group $G$ with $G/N$ almost simple, where $Nunlhd G$ is the solvable socle. Suppose $theta$ is a character of $N$ that has some degree and I want $G$ to have an irreducible constituent of $theta^G$ in $G$. I want $I_G(theta)$ to have some index.



How can I construct this group or rather show that it does not exist?




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    up vote
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    down vote

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    In trying to eliminate some graphs associated with character degrees of finite groups, one comes across a challenge of not having enough tools to do the same. This raises a question on whether one can construct a group with favourable outcome. For example:



    Suppose I need to construct a group $G$ with $G/N$ almost simple, where $Nunlhd G$ is the solvable socle. Suppose $theta$ is a character of $N$ that has some degree and I want $G$ to have an irreducible constituent of $theta^G$ in $G$. I want $I_G(theta)$ to have some index.



    How can I construct this group or rather show that it does not exist?




    characters




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      In trying to eliminate some graphs associated with character degrees of finite groups, one comes across a challenge of not having enough tools to do the same. This raises a question on whether one can construct a group with favourable outcome. For example:



      Suppose I need to construct a group $G$ with $G/N$ almost simple, where $Nunlhd G$ is the solvable socle. Suppose $theta$ is a character of $N$ that has some degree and I want $G$ to have an irreducible constituent of $theta^G$ in $G$. I want $I_G(theta)$ to have some index.



      How can I construct this group or rather show that it does not exist?




      characters




      share|cite|improve this question











      In trying to eliminate some graphs associated with character degrees of finite groups, one comes across a challenge of not having enough tools to do the same. This raises a question on whether one can construct a group with favourable outcome. For example:



      Suppose I need to construct a group $G$ with $G/N$ almost simple, where $Nunlhd G$ is the solvable socle. Suppose $theta$ is a character of $N$ that has some degree and I want $G$ to have an irreducible constituent of $theta^G$ in $G$. I want $I_G(theta)$ to have some index.



      How can I construct this group or rather show that it does not exist?





      characters





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 24 at 13:31









      Donnie Munyao Kasyoki

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