query: Show that $K$ is normal in $HK$.
positive_passages.docid: 22477
positive_passages.text: If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
negative_passages.docid: 102979
negative_passages.text: If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
negative_passages.docid: 12293
negative_passages.text: Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
negative_passages.docid: 25832
negative_passages.text: Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
negative_passages.docid: 134439
negative_passages.text: Proving function is $C^k$
negative_passages.docid: 139096
negative_passages.text: $|AxA|$ is a constant implies normal subgroup
negative_passages.docid: 22297
negative_passages.text: Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
negative_passages.docid: 138167
negative_passages.text: Image of a normal space under a closed and continuous map is normal
negative_passages.docid: 30327
negative_passages.text: $\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
negative_passages.docid: 54690
negative_passages.text: Proving normality of affine schemes
negative_passages.docid: 37971
negative_passages.text: Prove that the center of a group is a normal subgroup
negative_passages.docid: 113013
negative_passages.text: Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
negative_passages.docid: 121587
negative_passages.text: Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
negative_passages.docid: 115204
negative_passages.text: Show that SO(n) is a normal subgroup of O(n)
negative_passages.docid: 52105
negative_passages.text: Prove that $HK$ is a subgroup iff $HK=KH$.
negative_passages.docid: 12802
negative_passages.text: Proof of correctness of normal equation
negative_passages.docid: 73419
negative_passages.text: For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.