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1answer
313 views

Irreducible representation decomposition

Any faithful finite group representation can be written as a sum of irreducible representations $\rho = \oplus_{i} a_i \rho_i$ such that $Ker(\rho)=0=\bigcap_i Ker(\rho_i)$ - is this sufficient to ...
2
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1answer
101 views

Is the estimation of number's name's length and comma-grouping feasible?

I am thinking in a mathematical problem that probably is already formulated and even solved. It is about big integers and someting else. Let n be an integer positive number. For n := 1,000 we have ...
4
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1answer
135 views

The natural inclusion of an infinite abelian group $G$ into $\widehat{\widehat{G}}$

I was recently trying to think of a simple example that demonstrates that the natural inclusion of an abelian group $G$ into ...
8
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1answer
223 views

An exercise involving characters

Suppose $p$ is a prime, $\chi$ and $\lambda$ are characters on $\mathbb{F}_p$. How can I show that $\sum_{t\in\mathbb{F}_p}\chi(1-t^m)=\sum_{\lambda}J(\chi,\lambda)$ where $\lambda$ varies over all ...