query: Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
positive_passages.docid: 41085
positive_passages.text: Conjugate subgroup strictly contained in the initial subgroup?
negative_passages.docid: 145600
negative_passages.text: Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
negative_passages.docid: 106562
negative_passages.text: Is $3 \ge 1$ or is it just $3 > 1$?
negative_passages.docid: 65744
negative_passages.text: How can I Prove that H=G or K=G
negative_passages.docid: 98921
negative_passages.text: Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
negative_passages.docid: 3756
negative_passages.text: If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
negative_passages.docid: 125582
negative_passages.text: Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.
negative_passages.docid: 150042
negative_passages.text: Prove $x^{-1}Hx$ is a subgroup of $G$
negative_passages.docid: 62077
negative_passages.text: Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
negative_passages.docid: 68705
negative_passages.text: Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
negative_passages.docid: 58033
negative_passages.text: $G\times H\cong G$ with $H$ non-trivial
negative_passages.docid: 35800
negative_passages.text: If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
negative_passages.docid: 146760
negative_passages.text: Prove that H is a subgroup of G
negative_passages.docid: 89659
negative_passages.text: $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
negative_passages.docid: 93157
negative_passages.text: If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
negative_passages.docid: 100465
negative_passages.text: Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
negative_passages.docid: 83273
negative_passages.text: Show that $o(gHg^{-1})=o(H)$