Prove that a fundamental group is equal to a semidirect product.
141190
Fundamental group of mapping torus?
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
154878
Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
86025
Nonabelian semidirect products of order $pq$?
142698
Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
29269
fundamental group of $GL^{+}_n(\mathbb{R})$
125833
Semidirect Products with GAP
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
55652
Fundamental group of the torus
84198
Step in Proof of Cardinality of Product of two Groups
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
99346
Prove a result on transitive group actions.
58707
Prove Quotient Group Isomorphism
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
65744
How can I Prove that H=G or K=G