Prove $[G:A] = [G:B]\cdot [B:A]$ if $A\leqslant B\leqslant G$
58937
Finite Index of Subgroup of Subgroup
111515
Proving that $-a=(-1)\cdot a$
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
99346
Prove a result on transitive group actions.
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
62455
Prove Equivalence Relation in G
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
14277
Proving $f(x)=x\cdot |x|$ is a bijection
110313
Prove that $\gcd(f(x),g(x)) = 1$.