Let $a$ and $b$ belong to a group. If $|a|$ and $|b|$ are relatively prime, show that $\langle a \rangle \cap \langle b \rangle = \{e \}$
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
29445
Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
27086
proof for $\langle q| p \rangle = e^{ipq}$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
134687
Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?