query: Finite Abelian group with the given property
positive_passages.docid: 151619
positive_passages.text: A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
negative_passages.docid: 102971
negative_passages.text: Product of all elements of a finite group with an unique element of order 2
negative_passages.docid: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 108330
negative_passages.text: Product of all elements in finite abelian group equals its own inverse
negative_passages.docid: 43783
negative_passages.text: Abelian group (Commutative group)
negative_passages.docid: 145159
negative_passages.text: Finite group is abelian if the representatives of its conjugacy classes commute
negative_passages.docid: 74586
negative_passages.text: Prove that every group of order $4$ is abelian
negative_passages.docid: 139100
negative_passages.text: A question on the group algebra $k[G]$ of a finite abelian group
negative_passages.docid: 42153
negative_passages.text: Every finite abelian group is the Galois group of some finite extension of the rationals
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 5297
negative_passages.text: If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
negative_passages.docid: 66510
negative_passages.text: A group is abelian if and only if the center of the group is all the group
negative_passages.docid: 31380
negative_passages.text: Exponent and abelian groups
negative_passages.docid: 122335
negative_passages.text: Abelian $p$-group with unique subgroup of index $p$
negative_passages.docid: 130993
negative_passages.text: 4 Element abelian subgroup of S5.
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group