Group theory: prove that there is an element $s \in S$ such that $f(s) = s$
70967
Permutation with prime order, fixed point
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
44100
Prove that identity element is unique
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
98542
Prove that $H$ is a subgroup of an abelian group $G$
99346
Prove a result on transitive group actions.
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
7121
If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
137931
Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
75614
Proving that $n|m\implies f_n|f_m$
3462
Proving a set of automorphisms of a group is a group under composition
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
149801
prove that $TS = ST$