Abstract
We verify the inductive Alperin–McKay condition introduced by the second author, for 2-blocks of the covering groups of finite simple non-abelian groups with cyclic defect groups.
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Broué M., Puig L.: A Frobenius theorem for blocks. Invent. Math. 56, 117–128 (1980)
Broué M., Puig L.: Characters and local structure in G-algebras. J. Algebra 63, 306–317 (1980)
Cabanes M.: Extensions of p-groups and construction of characters. Comm. Algebra 15, 1297–1311 (1987)
Cabanes M.: A note on extensions of p-blocks by p-groups and their characters J. Algebra 115, 445–449 (1988)
M. Cabanes and B. Späth, Equivariant character correspondences and inductive McKay condition for type A, to appear in J. reine angew. Math. (2015).
Dade E.C.: Blocks with cyclic defect groups. Ann. of Math. 84, 20–48 (1966)
Dade E.C.: Block extensions. Illinois J. Math. 17, 198–272 (1973)
L. Dornhoff, Group Representation Theory. Part B: Modular representation theory, Pure and Applied Mathematics, New York, 1972.
I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
Koshitani S., Späth B.: Clifford theory of characters in induced blocks. Proc. Amer. Math. Soc. 143, 3687–3702 (2015)
S. Koshitani and B. Späth, The inductive Alperin-McKay and blockwise Alperin Weight conditions for blocks with cyclic defect groups and odd primes. submitted.
Murai M.: On blocks of normal subgroups of finite groups. Osaka J. Math. 50, 1007–1020 (2013)
H. Nagao and Y. Tsushima, Representations of Finite Groups, Transl. from the Japanese. Academic Press, Inc., 1989.
G. Navarro, Characters and Blocks of Finite Groups, London Math. Soc. Lecture Note Series, Vol. 250. Cambridge University Press, Cambridge, 1998.
Navarro G., Späth B.: On Brauer’s height zero conjecture. J. Europ. Math. Soc. 16, 695–747 (2014)
Späth B.: A reduction theorem for the Alperin-McKay conjecture. J. reine angew. Math. 680, 153–184 (2013)
Späth B.: A reduction theorem for the Blockwise Alperin Weight conjecture. J. Group Theory 16, 159–220 (2013)
J. Thévenaz, G-Algebras and Modular Representation Theory, Oxford Mathematical Monographs, New York, 1995. Oxford Science Publications.
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S. Koshitani and B. Späth have been supported respectively by the Japan Society for Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C)23540007, 2011–2014, (C)15K04776, 2015–2018, and the ERC Advanced Grant 291512.
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Koshitani, S., Späth, B. The inductive Alperin–McKay condition for 2-blocks with cyclic defect groups. Arch. Math. 106, 107–116 (2016). https://doi.org/10.1007/s00013-015-0852-4
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DOI: https://doi.org/10.1007/s00013-015-0852-4