All Questions

For a prime $p$, let $G$ be a finite $p$-group and $F_{p}$ the field with $p$ elements. Let $A=\{a\in F_{p}G \mid a^{\sum_{x\in G}x}\neq 0\}$, where $F_pG$ is the group algebra of $G$ over $F_p$ and $...

I cannot find a finite group $G$ such that $\exists x\in \mathbb{Q}[G]$ with $x^2=2e$, where $\mathbb{Q}[G]$ is the group algebra of $G$ over $\mathbb{Q}$. I also could not prove it does not exist. ...

For $A$ a finite-dimensional algebra over a field $K$ Does there exist a finite group $G$, such that $A$ is a sub-algebra of $K[G]$ ? Where $K[G]$ denotes the group-algebra of $G$ over $K$. In case ...

Let $G$ be a finite group, and let $A$ and $B$ be two abelian subgroups of $G$. Let $K$ be a number field such that all characters of $A$ and of $B$ take values in $K$. Let $\mathcal{O}_K$ be the ring ...

Conjecture. There exists a function $f:\mathbb{N} \rightarrow \mathbb{N}$ such that if $\beta$ is a non-zero element of the complex group algebra $\mathbb{C}[G]$ of a finite group $G$ such that $1\...

Conjecture. There exists a function $f:\mathbb{N} \rightarrow \mathbb{N}$ such that if $\alpha$ and $\beta$ are non-zero elements of the complex group algebra $\mathbb{C}[G]$ of a finite group $G$ ...