query: Equivalent definition of normalizer of a group. Need help in proof.
positive_passages.docid: 41085
positive_passages.text: Conjugate subgroup strictly contained in the initial subgroup?
negative_passages.docid: 70373
negative_passages.text: Intersection of normal subgroups proof
negative_passages.docid: 101079
negative_passages.text: Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
negative_passages.docid: 158490
negative_passages.text: Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 63780
negative_passages.text: to show characteristic subgroup is normal in G
negative_passages.docid: 114522
negative_passages.text: Prove that identity is unique in a group
negative_passages.docid: 29717
negative_passages.text: Not sure how to go about this group theory proof
negative_passages.docid: 90584
negative_passages.text: Show set of affine transformations is a group
negative_passages.docid: 87265
negative_passages.text: If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
negative_passages.docid: 126771
negative_passages.text: Group element not taken to its inverse by any automorphism
negative_passages.docid: 64372
negative_passages.text: Do the isomorphism's of groups form an equivalence relation on the class of all groups?
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 85508
negative_passages.text: Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
negative_passages.docid: 49666
negative_passages.text: Generalization of index 2 subgroups are normal
negative_passages.docid: 18160
negative_passages.text: How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
negative_passages.docid: 121587
negative_passages.text: Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$