query: Is every group realized as the group of units of a ring?
positive_passages.docid: 61391
positive_passages.text: Which finite groups are the group of units of some ring?
negative_passages.docid: 145127
negative_passages.text: For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
negative_passages.docid: 39938
negative_passages.text: Subgroups of a cyclic group and their order.
negative_passages.docid: 26483
negative_passages.text: Group algebra ever a field?
negative_passages.docid: 89864
negative_passages.text: Units in finite polynomial rings
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 91997
negative_passages.text: Product of two subgroups the whole group?
negative_passages.docid: 139218
negative_passages.text: Is this group solvable?
negative_passages.docid: 75157
negative_passages.text: Every Group is a Fundamental Group
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 115585
negative_passages.text: Do Boolean rings always have a unit element?
negative_passages.docid: 133738
negative_passages.text: Can a ring without a unit element have a subring with a unit element?
negative_passages.docid: 18361
negative_passages.text: Does the unit generate the additive group in a unital ring with cyclic additive group?
negative_passages.docid: 32772
negative_passages.text: Proving units in a ring
negative_passages.docid: 151210
negative_passages.text: How can we find and categorize the subgroups of $\mathbb{R}$?
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?