$G$ finite group and $\mathbb{C}[G]$ its group ring, show: $K_i = \sum_{a_k\in cl_G(a_i)} a_k $, then $Z(\mathbb{C}[G])=span_\mathbb{C}(K_1,...,K_n)$
33728
Basis for Center of Group Ring
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
113259
The confusing nature of direct sum for finite abelian groups
146028
$GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
24181
Showing that $G$ is a group under an alternative operation.
107716
Show that $G$ is cyclic
111824
Sum of nilpotent and element is a unit in ring?
59211
Product of Finite Abelian Group
68201
Cyclic group of order $n$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
152071
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$