query: Proving normality of a subset from its generators
positive_passages.docid: 154878
positive_passages.text: Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 50900
negative_passages.text: Testing normality
negative_passages.docid: 151467
negative_passages.text: An infinite generating set of a finite dimensional vector space contains a basis
negative_passages.docid: 92249
negative_passages.text: Every finite set contains its supremum: proof improvement.
negative_passages.docid: 153072
negative_passages.text: Guessing a subset of $\{1,...,N\}$
negative_passages.docid: 80186
negative_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 37331
negative_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 111375
negative_passages.text: Normality of subgroups and Sylow groups under homomorphisms...
negative_passages.docid: 77791
negative_passages.text: Proving an inclusion related to algebraic sets and interpreting it
negative_passages.docid: 141895
negative_passages.text: Proving that a sequence is monotone
negative_passages.docid: 70373
negative_passages.text: Intersection of normal subgroups proof
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 135743
negative_passages.text: Collection of subset generating every pairs of elements
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 71133
negative_passages.text: prove inequlity about cardinality power sets
negative_passages.docid: 104308
negative_passages.text: Proving a set is a Sigma Algebra