Tag: group-theory
- If $n$ odd, does $\begin{pmatrix}\zeta&0\\ 0&\zeta^{-1}\end{pmatrix}, \begin{pmatrix}0&-1\\ 1&0\end{pmatrix}$ generate the dihedral group
- Are there problems with this corollary of Schur’s Lemma
- Proving a non-cyclic $G$ has a cyclic subgroup of index $2$ and $G\cong D_k.$
- What’s an automorphism of a function
- A quick, more elementary way to show $(\mathbb{Z}/16 \mathbb{Z})^{\times} \cong C_4 \times C_2$
- Abelian + normal $\implies$ central
- How to see that $o(G) = p^n$ without using the fundamental theorem of finitely generated abelian groups
- Are the character tables for $Z$-groups known
- For every subgroup $H$ of a finite abelian group $ G$ there exist an endomorphism $\phi$ with $\text{Im}(\phi)=H$
- Need help with proof of property related to group rings.