Prove that the center of group G is a subgroup of G.
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
154398
Show that H is a subgroup of G
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
23533
All subgroups normal $\implies$ abelian group
33728
Basis for Center of Group Ring
114522
Prove that identity is unique in a group
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
51359
Prove that every subgroup of an abelian group is a normal subgroup.
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
66510
A group is abelian if and only if the center of the group is all the group
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
102622
K is a subgroup of G. Show that K is not a normal subgroup
99346
Prove a result on transitive group actions.
70373
Intersection of normal subgroups proof
79933
Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group.
46863
Show that $g$ is injective
142228
Proof that a subset closed under group operation of a finite group is a subgroup