Proof that a group is a group
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
124237
Group equals union of three subgroups
117701
Let $G$ be a group and $X$ set. $a,b \in X$ are in the same orbit, so show that $stab(a) \cong stab (b)$
150007
Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
112407
Set of left cosets is a group
103002
Group equals union of two subgroups
11003
Proving that $G/N$ is an abelian group
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
46116
Proof of the First Isomorphism Theorem for Groups
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
90332
Prove that that $U(n)$ is an abelian group.
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
24181
Showing that $G$ is a group under an alternative operation.