$x^2=e$ implies that $|G|=2^n$
60982
Group where every element is order 2
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
98968
$X$ is algebraic over $E$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
54369
Proof of $n^2 \leq 2^n$.
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
22073
Prove by induction that $n^2<n!$
152741
Cardinal of a group $G$ such that for all $x\in G$ we have $x^2=e$
62455
Prove Equivalence Relation in G
62177
Prove that: $2^n < n!$ Using Induction
23946
Prove the definitions of $e$ to be equivalent
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.