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Communications in Algebra Volume 52, 2024 - Issue 7
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Research Article

Fuchs’ problem for linear groups

Keir LockridgeDepartment of Mathematics, Gettysburg College, Gettysburg, Pennsylvania, USACorrespondence[email protected]
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Jacob TerkelDepartment of Mathematics, Gettysburg College, Gettysburg, Pennsylvania, USAView further author information
Pages 2892-2902 | Received 28 Aug 2023, Accepted 19 Jan 2024, Published online: 06 Feb 2024

References

  • Chebolu, S. K., Lockridge, K. (2015). Fuchs’ problem for indecomposable abelian groups. J. Algebra 438:325–336. DOI: 10.1016/j.jalgebra.2015.05.011.
  • Chebolu, S. K., Lockridge, K. (2017). Fuchs’ problem for dihedral groups. J. Pure Appl. Algebra 221(4):971–982. DOI: 10.1016/j.jpaa.2016.08.015.
  • Chebolu, S. K., Lockridge, K. (2017). How many units can a commutative ring have? Amer. Math. Monthly 124(10):960–965.
  • Chebolu, S. K., Lockridge, K. (2019). Fuchs’ problem for p-groups. J. Pure Appl. Algebra 223(11):4652–4666. DOI: 10.1016/j.jpaa.2019.02.008.
  • Chebolu, S. K., Mayers, M. (2013). What is special about the divisors of 12? Math. Mag. 86(2):143–146. DOI: 10.4169/math.mag.86.2.143.
  • Ditor, S. Z. (1971). On the group of units of a ring. Amer. Math. Monthly 78:522–523. DOI: 10.2307/2317760.
  • Davis, C., Occhipinti, T. (2014). Which alternating and symmetric groups are unit groups? J. Algebra Appl. 13(3):1350114, 12. DOI: 10.1142/S0219498813501144.
  • Davis, C., Occhipinti, T. (2014). Which finite simple groups are unit groups? J. Pure Appl. Algebra 218(4):743–744. DOI: 10.1016/j.jpaa.2013.08.013.
  • Fuchs, L. (1960). Abelian Groups. International Series of Monographs on Pure and Applied Mathematics. New York-Oxford-London-Paris: Pergamon Press.
  • The GAP Group. (2022). GAP–Groups, Algorithms, and Programming, Version 4.12.1.
  • Gilmer, Jr., R. W. (1963). Finite rings having a cyclic multiplicative group of units. Amer. J. Math. 85:447–452. DOI: 10.2307/2373134.
  • Lockridge, K., Terkel, J. (2023). GAP/SageMath code. https://cocalc.com/klockrid/main/SL2F3.
  • Miller, G. A. (1903). On the holomorph of a cyclic group. Trans. Amer. Math. Soc. 4(2):153–160. DOI: 10.1090/S0002-9947-1903-1500633-9.
  • Mills, W. H. (1961). Decomposition of holomorphs. Pac. J. Math. 11:1443–1446. DOI: 10.2140/pjm.1961.11.1443.
  • Pearson, K. R., Schneider, J. E. (1970). Rings with a cyclic group of units. J. Algebra 16:243–251. DOI: 10.1016/0021-8693(70)90030-X.
  • SageMath. 2022. The Sage Mathematics Software System (Version 9.6). https://www.sagemath.org.
  • Swartz, E., Werner, N. J. (2022). Corrigendum to “Fuchs’ problem for 2-groups” [J. Algebra 556 (2020) 225-245]. J. Algebra 608:25–36. DOI: 10.1016/j.jalgebra.2020.02.025.

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