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We count the number of lifts of an irreducible π-partial character that lies in a block with a cyclic defect group.
[1]Cliff, G. H., ‘On modular representations of p-solvable groups’, J. Algebra47 (1977), 129–137.CrossRefGoogle Scholar
[2]
[2]Cossey, J. P., ‘Bounds on the number of lifts of a Brauer character in a p-solvable group’, J. Algebra312 (2007), 699–708.CrossRefGoogle Scholar
[3]
[3]Cossey, J. P., ‘Vertices and normal subgroups in solvable groups’, J. Algebra321 (2009), 2962–2969.CrossRefGoogle Scholar
[4]
[4]Dade, E. C., ‘Extending endo-permutation modules’, Preprint.Google Scholar
[5]
[5]Dade, E. C., ‘A correspondence of characters’, Proc. Sympos. Pure Math.37 (1980), 401–403.CrossRefGoogle Scholar
[6]
[6]Dornhoff, L., Group Representation Theory Part B (Marcel Dekker, New York, 1972).Google Scholar
[7]
[7]Erdmann, K., ‘Blocks and simple modules with cyclic vertices’, Bull. Lond. Math. Soc.9 (1977), 216–218.CrossRefGoogle Scholar
[8]
[8]Feit, W. and Thompson, J., ‘Groups which have a faithful representation of degree less than (p−1)/2’, Pacific J. Math.11 (1961), 1257–1262.CrossRefGoogle Scholar
[9]
[9]Gajendragadkar, D., ‘A characteristic class of characters of finite π-separable groups’, J. Algebra59 (1979), 237–259.CrossRefGoogle Scholar
[10]
[10]Hai, J., ‘The extension of the first main theorem for π-blocks’, Sci. China Ser. A49 (2006), 620–625.CrossRefGoogle Scholar
[11]
[11]Isaacs, I. M., ‘Fong characters in π-separable groups’, J. Algebra99 (1986), 89–107.CrossRefGoogle Scholar
[12]
[12]Isaacs, I. M., ‘Partial characters of π-separable groups’, in: Representation Theory of Finite Groups and Finite Dimensional Algebras (Bielefield, 1991), Progress in Mathematics, 95 (Birkhäuser, Basel, 1991), pp. 273–287.CrossRefGoogle Scholar
[13]
[13]Isaacs, I. M. and Navarro, G., ‘Weights and vertices for characters of π-separable groups’, J. Algebra177 (1995), 339–366.CrossRefGoogle Scholar
[14]
[14]Manz, O. and Wolf, T. R., Representations of Solvable Groups, London Mathematical Society Lecture Notes Series, 185 (Cambridge University Press, Cambridge, 1993).CrossRefGoogle Scholar
[15]
[15]Navarro, G., Characters and Blocks of Finite Groups (Cambridge University Press, Cambridge, 1998).CrossRefGoogle Scholar
[16]
[16]Puig, L., ‘Local extensions in endo-permutation modules split: a proof of Dade’s theorem’, in: Seminaire sur les Groupes Finis (Seminaire Claude Chevalley), Tome III, Publications Mathématiques de l’Université Paris VII, 25 (Univ. Paris VII, Paris, 1986), pp. 199–205.Google Scholar
[17]
[17]Slattery, M. C., ‘Pi-blocks of pi-separable groups, I’, J. Algebra102 (1986), 60–77.CrossRefGoogle Scholar
[18]
[18]Slattery, M. C., ‘Pi-blocks of pi-separable groups, II’, J. Algebra124 (1989), 236–269.CrossRefGoogle Scholar
[19]
[19]Turull, A., ‘Above the Glauberman correspondence’, Adv. Math.217 (2008), 2170–2205.CrossRefGoogle Scholar