Group action with a single orbit has a $g \in G$ with no fixed points
63691
G acts on X transitively, then there exists some element that does not have any fixed points
19720
A normal subgroup intersects the center of the $p$-group nontrivially
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
90764
Prove that the fundamental group of the circle is non-trivial if the fundamental group of a space $X$ is non-trivial
88726
Problem about solvable groups
37635
Diffeomorphism group of the unit circle
43004
Why are there $|G/G'|$ 1-dimensional representations of $G$?
80381
Groups with "few" subgroups
24181
Showing that $G$ is a group under an alternative operation.
113919
Surface of genus $g$ does not retract to circle (Hatcher exercise)
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
129830
A group with no proper non-trivial subgroups
42582
Infinite group with only two conjugacy classes
103613
Two Claims about Symplectic Group Actions
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
137233
$f$ is irreducible $\iff$ $G$ act transitively on the roots
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$