Show that $G$ is not simple.
35226
No simple group of order $1,000,000$
11957
G is the product of its Sylow subgroups
9612
Frattini subgroup $Φ ( G )$ is not trivial
83273
Show that $o(gHg^{-1})=o(H)$
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
27728
Question on a homomorphism of a set G.
58033
$G\times H\cong G$ with $H$ non-trivial
129830
A group with no proper non-trivial subgroups
48780
How t show $f=g$ almost everywhere
83915
Showing that a function is not differentiable
75479
Proving that this function is continuous on $G\times G$
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
65744
How can I Prove that H=G or K=G
46863
Show that $g$ is injective
57883
Example of a Subgroup That Is Not Normal
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$