Morita equivalences between some blocks for 𝑝-solvable groups

Zhou, Yuanyang

doi:10.1090/S0002-9939-05-08038-X

Morita equivalences between some blocks for $p$-solvable groups
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by Yuanyang Zhou PDF

Proc. Amer. Math. Soc. 133 (2005), 3133-3142 Request permission

Abstract:

We prove that any Morita equivalence between some blocks with Abelian defect groups and cyclic inertia quotients for $p$-solvable groups is basic.

References

P. Fong, On the characters of $p$-solvable groups, Trans. Amer. Math. Soc. 98 (1961), 263–284. MR 120297, DOI 10.1090/S0002-9947-1961-0120297-5
M. Hertweck, Units of $p$-power order in principal blocks of $p$-constrained groups, preprint.
Burkhard Külshammer, On $p$-blocks of $p$-solvable groups, Comm. Algebra 9 (1981), no. 17, 1763–1785. MR 631888, DOI 10.1080/00927878108822682
Burkhard Külshammer and Lluís Puig, Extensions of nilpotent blocks, Invent. Math. 102 (1990), no. 1, 17–71. MR 1069239, DOI 10.1007/BF01233419
M. E. Harris and M. Linckelmann, Splendid derived equivalences for blocks of finite $p$-solvable groups, J. London Math. Soc. (2) 62 (2000), no. 1, 85–96. MR 1771852, DOI 10.1112/S0024610700008966
Lluís Puig, Pointed groups and construction of characters, Math. Z. 176 (1981), no. 2, 265–292. MR 607966, DOI 10.1007/BF01261873
L. Puig, Notes on $\mathcal {O}^*$-groups, preprint.
Lluís Puig, On the local structure of Morita and Rickard equivalences between Brauer blocks, Progress in Mathematics, vol. 178, Birkhäuser Verlag, Basel, 1999. MR 1707300
Lluís Puig, Pointed groups and construction of modules, J. Algebra 116 (1988), no. 1, 7–129. MR 944149, DOI 10.1016/0021-8693(88)90195-0
Lluís Puig, Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), no. 1, 77–116. MR 943924, DOI 10.1007/BF01393688
Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237, DOI 10.1007/978-1-4757-5673-9
Jacques Thévenaz, $G$-algebras and modular representation theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. Oxford Science Publications. MR 1365077