Prove that Group Ring RG is not a Division Ring for R commutative and G a finite group
26483
Group algebra ever a field?
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
88307
Commutative property of ring addition
116737
An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
151803
Prove that $R$ is commutative
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
14055
How to show that a finite commutative ring without zero divisors is a field?
87946
Proving that the unities of a ring form a group under multiplication
6385
Minimal counterexamples of the isomorphism problem for integral group rings
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic