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Communications in Algebra Volume 48, 2020 - Issue 1
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Original Articles

The strong Frobenius numbers for cyclic defect blocks are equal to one

Markus LinckelmannDepartment of Mathematics, City, University of London, London, UKCorrespondence[email protected]
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Pages 141-148 | Received 10 Dec 2018, Accepted 16 May 2019, Published online: 19 Jul 2019

References

  • Benson, D. J., Kessar, R. (2007). Blocks inequivalent to their Frobenius twists. J. Algebra. 315(2):588–599. DOI:10.1016/j.jalgebra.2007.03.044.
  • Boltje, R., Kessar, R., Linckelmann, M. (2019). On Picard groups of blocks of finite groups. J. Algebra. (To appear). DOI:10.1016/j.jalgebra.2019.02.045.
  • Curtis, C. W., Reiner, I. (1987). Methods of Representation Theory, Vol. II. New York, London, Sydney: Wiley.
  • Dade, E. C. (1966). Blocks with cyclic defect groups. Ann. Math. 84(1):20–48. DOI:10.2307/1970529.
  • Eaton, C. W., Eisele, F., Livesey, M. (2018). Donovan’s conjecture, blocks with abelian defect groups and discrete valuation rings. arXiv:1809.08152.
  • Eaton, C. W., Livesey, M. (2019). Towards Donovan’s conjecture for abelian defect groups. J. Algebra. 519:39–61. DOI:10.1016/j.jalgebra.2018.09.043.
  • Eaton, C. W., Livesey, M. (2018). Donovan’s conjecture and blocks with abelian defect groups. Proc. Amer. Math. Soc. 147(3):963–970. DOI:10.1090/proc/14316.
  • Farrell, N. (2017). On the Morita Frobenius numbers of blocks of finite reductive groups. J. Algebra. 471:299–318. DOI:10.1016/j.jalgebra.2016.08.043.
  • Farrell, N., Kessar, R. (2018). Rationality of blocks of quasi-simple finite groups. arXiv:1805.02015.
  • Kessar, R. (2004). A remark on Donovan’s conjecture. Arch. Math. 82:391–394.
  • Kessar, R., Linckelmann, M. (2010). On stable equivalences and blocks with one simple module. J. Algebra. 323(6):1607–1621. DOI:10.1016/j.jalgebra.2010.01.006.
  • Linckelmann, M. (1994). The source algebras of blocks with a Klein four defect group. J. Algebra. 167(3):821–854. DOI:10.1006/jabr.1994.1214.
  • Linckelmann, M. (1996). Stable equivalences of Morita type for self-injective algebras and p-groups. Math. Z. 223(1):87–100. DOI:10.1007/PL00004556.
  • Linckelmann, M. (2001). On splendid derived and stable equivalences between blocks of finite groups. J. Algebra. 242(2):819–843. DOI:10.1006/jabr.2001.8812.
  • Linckelmann, M. (2018). On automorphisms and focal subgroups of blocks. In: Carlson, J. F., et al., eds. Geometric and Topological Aspects of the Representation Theory of Finite Groups. Springer Proceedings in Mathematics and Statistics, Vol. 242. Cham: Springer, pp. 235–249.
  • Linckelmann, M. (2018). The Block Theory of Finite Group Alegbras I. London Math. Soc. Student Texts, Vol. 91. Cambridge: Cambridge University Press.
  • Linckelmann, M. (2018). The Block Theory of Finite Group Alegbras II. London Math. Soc. Student Texts, Vol. 92. Cambridge: Cambridge University Press.
  • Puig, L. (1991). Une correspondance de modules pour les blocs à groupes de défaut abéliens. Geom. Dedicata. 37(1):9–43. DOI:10.1007/BF00150403.
  • Puig, L. (1999). On the Local Structure of Morita and Rickard Equivalences Between Brauer Blocks. Prog. Math., Vol. 178. Basel: Birkhäuser Verlag.
  • Scott, L. L. (1990). Unpublished notes. DOI:10.1093/notesj/s12-II.32.114-b.
  • Serre, J. P. (1979). Local fields. In: Graduate Texts in Mathematics, Vol. 67. New York: Springer-Verlag.

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