query: Transitive subgroup of $S_n$ with n prime and a transposition is always the entire $S_n$
positive_passages.docid: 35472
positive_passages.text: Transitive subgroup of symmetric group $S_n$ containing an $(n-1)$-cycle and a transposition
negative_passages.docid: 59811
negative_passages.text: Finite Abelian groups with the same number of elements for all orders are isomorphic
negative_passages.docid: 96878
negative_passages.text: A finite group with the property that all of its proper subgroups are abelian
negative_passages.docid: 142413
negative_passages.text: Normal Subgroups of $SU(n)$
negative_passages.docid: 131516
negative_passages.text: Subgroup generated by n-th powers of elements
negative_passages.docid: 78283
negative_passages.text: Centralizer of a given element in $S_n$?
negative_passages.docid: 64408
negative_passages.text: Subgroup of $\mathbb{Q}$ with finite index
negative_passages.docid: 122271
negative_passages.text: A subset of a transitive set is transitive
negative_passages.docid: 72150
negative_passages.text: Union of the conjugates of a proper subgroup
negative_passages.docid: 118337
negative_passages.text: Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$
negative_passages.docid: 4838
negative_passages.text: For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
negative_passages.docid: 151130
negative_passages.text: When is the product of $n$ subgroups a subgroup?
negative_passages.docid: 148413
negative_passages.text: Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 24561
negative_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 11731
negative_passages.text: Normal subgroups of $S_4$
negative_passages.docid: 33945
negative_passages.text: Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups