Let $G$ be a finite semigroup .Prove that there exist $x\in G $ such that $x^2=x$
7536
Is there an idempotent element in a finite semigroup?
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
120288
Semigroup isomorphism
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
46342
Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism
61550
Existence of elements of order $p^k$ in a finite group
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
68732
Prove that a semigroup satisfying $a^pb^q=ba$ is commutative
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
141125
Group with order $p^2$ must be abelian . How to prove that?