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Questions about the branch of algebra that deals with groups.

1 vote
2 answers
205 views

Galois stability of characters

Let $G$ be a finite cyclic group and $\widehat{G}$ the character group. Let $S \subset \widehat{G}$ be a Galois-stable subset i.e. if $\chi \in S$, then the Galois conjugates $\chi^{\sigma} \in S$ for …
4 votes
0 answers
199 views

Linear combination of characters

For each $i \in \mathbb{N}$, let $G_{i}$ be a finite abelian group and $\widehat{G_{i}}$ the $\overline{\mathbb{Q}}$-valued character group of $G_{i}$. Suppose that $|G_{i}| \rightarrow \infty$ as $i …