If every Sylow subgroup of G is a normal subgroup, show that G is isomorphic to the product of its Sylow subgroups.
11957
G is the product of its Sylow subgroups
138406
If N and every subgroup of N is normal in G then G/N is abelian .
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
102622
K is a subgroup of G. Show that K is not a normal subgroup
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
29736
Sylow Subgroups of a Dihedral Group
91997
Product of two subgroups the whole group?
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
2174
Proving that HK is a subgroup when K is normal
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
142413
Normal Subgroups of $SU(n)$
103423
Normal subgroup where G has order prime