query: Algebraic Groups Problem
positive_passages.docid: 92064
positive_passages.text: A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$
negative_passages.docid: 80849
negative_passages.text: There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
negative_passages.docid: 76943
negative_passages.text: Existence of subgroup of order six in $A_4$
negative_passages.docid: 154398
negative_passages.text: Show that H is a subgroup of G
negative_passages.docid: 22444
negative_passages.text: Normal subgroups of dihedral groups
negative_passages.docid: 146278
negative_passages.text: Automorphism group of direct product of groups
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 103829
negative_passages.text: Find the subgroups of A4
negative_passages.docid: 56650
negative_passages.text: Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
negative_passages.docid: 8602
negative_passages.text: Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
negative_passages.docid: 112371
negative_passages.text: Computing irreducible components of algebraic set
negative_passages.docid: 90511
negative_passages.text: Commutator subgroup of a dihedral group.
negative_passages.docid: 33152
negative_passages.text: Classifying groups of order 18
negative_passages.docid: 148904
negative_passages.text: Groups of order $p^3$
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$
negative_passages.docid: 11957
negative_passages.text: G is the product of its Sylow subgroups