Advanced search
Publication Cover
Communications in Algebra Volume 52, 2024 - Issue 10
Submit an article Journal homepage
13
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A class of finite p-groups and the normalized unit groups of group algebras

Yulei Wanga Department of Mathematics, Henan University of Technology, Zhengzhou, P. R. ChinaCorrespondence[email protected]
View further author information
&
Heguo Liub Department of Mathematics, Hainan University, Haikou, P. R. ChinaView further author information
Pages 4272-4294 | Received 08 Jan 2024, Accepted 24 Feb 2024, Published online: 02 May 2024

References

  • Balogh, Z. (2020). The structure of the unit group of some group algebras. Miskolc Math. Notes 21(2):615–620. DOI: 10.18514/MMN.2020.3406.
  • Balogh, Z., Bovdi, A. (2004). Group algebras with unit group of class p. Publ. Math. Debrecen 65(3–4):261–268. DOI: 10.5486/PMD.2004.3239.
  • Blackburn, S. R. (1999). Groups of prime power order with derived subgroup of prime order. J. Algebra 219: 625–657. DOI: 10.1006/jabr.1998.7909.
  • Bornand, D. (2009). Elementary Abelian Subgroups in p-groups of Class 2. Lausanne: École Polytechnique Fédérale de Lausanne.
  • Bovdi, A. (1998). The group of units of a group algebra of characteristic p. Publ. Math. Debrecen 52(1–2):193–244. DOI: 10.5486/PMD.1998.2009.
  • Bovdi, A., Kurdics, J. (1999). Lie properties of the group algebra and the nilpotency class of the group of units. J. Algebra 212(1):28–64. DOI: 10.1006/jabr.1998.7617.
  • Bovdi, A., Patay, Z. (2003). Units in group algebras of finite p-groups. J. Math. Sci. 116(1):2887–2893. DOI: 10.1023/A:1023438307017.
  • Brauer, R. (1956). Zur darstellungstheorie der gruppen endlicher ordnung. Math. Z. 63:406–444. DOI: 10.1007/BF01187950.
  • Dietz, J. (2001). Automorphisms of p-group given as cyclic-by elementary abelian central extensions. J. Algebra 242:417–432. DOI: 10.1006/jabr.2001.8826.
  • Hall, P. (1940). The classification of prime-power groups. J. Reine Angew. Math. 182:130–141. DOI: 10.1515/crll.1940.182.130.
  • Johnson, D. L. (1978). The modular group ring of a finite p-group. Proc. Amer. Math. Soc. 68(1):19–22.
  • Lee, G. T. (2010). Group Identities on Units and Symmetric Units of Group Rings. London: Springer.
  • Liu, H. G., Wang, Y. L. (2010). The automorphism group of a generalized extraspecial p-gorup. Sci. China Math. 53(2):315–334. DOI: 10.1007/s11425-009-0151-2.
  • Liu, H. G., Wang, Y. L. (2016). Automorphism groups of some finite p-groups. Algebra Colloq. 23(4):623–650. DOI: 10.1142/S1005386716000535.
  • Milies, C. P., Sehgal, S. K. (2002). An Introduction to Group Rrings. Dordrecht-Boston-London: Kluwer Academic Publishers.
  • Robinson, D. J. S. (1996). A Course in the Theory of Groups, 2nd ed. New York: Springer-Verlag.
  • Sandling, R. (1984). Units in the modular group algebra of a finite abelian p-group. J. Pure Appl. Algebra 33:337–346. DOI: 10.1016/0022-4049(84)90066-5.
  • Sandling, R. (1989). The modular group algebra of a central-elementary-by-abelian p-group. Arch. Math. 52:22–27. DOI: 10.1007/BF01197966.
  • Wang, Y. L., Liu, H. G. (2012). The generalization of the theorems of Winter and Dietz. Chin. Ann. Math. Ser. A 33A(5):609–630. (In Chinese.)
  • Wang, Y. L., Liu, H. G. (2024). The unitary subgroups of group algebras of a class of finite 2-groups with the derived subgroup of order 2. Sci. China Math. 67:1–30. DOI: 10.1007/s11425-023-2156-7.
  • Winter, D. (1972). The automorphism group of an extraspecial p-group. Rocky Mountain J. Math. 2:159–168. DOI: 10.1216/RMJ-1972-2-2-159.
  • Xu, M. Y., Qu, H. P. (2010). Finite p-groups. Beijing: Peking University Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.