|
|||||
 |
|
|
|
|
|
|
|
Fuchs' problem
for small groups
Joshua A. Carr, William J. Cook and Lindsey M. Wise |
|
Vol. 17 (2024), No. 3, 441–463
|
Abstract |
|
Fuchs’ problem asks which groups are realizable as the unit group of a ring. We solve Fuchs’ problem for dicyclic groups realized by finite rings. We also survey known results and give a complete list of realizable groups of order at most 15. For these realizable groups, we provide a ring in every viable characteristic. Consequently, we show the dicyclic group of order 12 is the smallest realizable group that cannot be realized by a finite ring. |
PDF Access Denied
We have not been able to recognize your IP address
18.226.169.169
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 30.00:
Keywords
Fuchs' problem, group of units, dicyclic groups
|
Mathematical Subject Classification
Primary: 16U60
Secondary: 20C05
|
Milestones
Received: 5 April 2022
Revised: 22 December 2022
Accepted: 26 April 2023
Published: 17 July 2024
Communicated by Kenneth S. Berenhaut
|
Authors |
| Joshua A. Carr | |
| Wilkes Community College Wilkesboro, NC United States |
|
| William J. Cook | |
| Appalachian State University Boone, NC United States |
|
| Lindsey M. Wise | |
| University of Southern
California Los Angeles, CA United States |
|
| © 2024 MSP (Mathematical Sciences Publishers). |
