Clifford Theory of a Finite Group that Contains a Defect 0 p-Block of a Normal Subgroup

REFERENCES

• Broué , M. , Olsson , J. ( 1986 ). Subpairs multiplicities in finite groups . J. Reine Angew. Math. 371 : 125 – 143 .
   Web of Science ®Google Scholar
• Broué , M. ( 1978 ). Radical, Hauteurs, p-sections et blocs . Ann. of Math. 107 : 89 – 107 .
   Web of Science ®Google Scholar
• Broué , M. ( 1990 ). Isométries, parfaites, types de blocs, catégories dérivees . Asterisque 181–182 : 61 – 92 .
   Google Scholar
• Cabanes , M. ( 1988 ). A note on extensions of p-blocks by p-groups and their characters . J. Algebra 115 : 445 – 449 .
   Google Scholar
• Dade , E. C. ( 1980 ). A correspondence of characters . Proc. Sympos. Pure Math. Vol. 37, Santa Cruz, 1980. Providence, RI: A.M.S., pp. 401–404 .
   Google Scholar
• Dade , E. C. Extending endo-permutation modules. Manuscript .
   Google Scholar
• Feit , W. ( 1982 ). The Representation Theory of Finite Groups . Amsterdam–New York–Oxford : North-Holland .
   Google Scholar
• Harris , M. E. ( 2004 ). Glauberman-Watanabe corresponding p-blocks of finite groups with normal defect groups are Morita equivalent . Trans. of the A. M. S. 357 ( 1 ): 309 – 335 .
   Web of Science ®Google Scholar
• Harris , M. E. ( 2007 ). A Morita equivalence for blocks of finite p-solvable groups in the Glauberman-Isaacs-Watanabe correspondence context . J. Group Theory 10 : 15 – 34 .
   Web of Science ®Google Scholar
• Harris , M. E. ( 2007 ). Ordinary induction from a subgroup and finite group block theory . Osaka J. Math. 44 : 147 – 158 .
   Web of Science ®Google Scholar
• Harris , M. E. , Knörr , R. ( 1985 ). Brauer correspondence for covering blocks of finite groups . Comm. in Algebra 13 : 1213 – 1218 .
   Web of Science ®Google Scholar
• Harris , M. E. , Linckelmann , M. ( 2000 ). Splended derived equivalences for blocks of finite p-solvable groups . J. London Math. Soc. 62 : 85 – 96 .
   Web of Science ®Google Scholar
• Huppert , B. ( 1967 ). Endliche Gruppen I . Berlin : Springer Verlag .
   Google Scholar
• Isaacs , I. M. ( 1976 ). Character Theory of Finite Groups . New York : Academic Press .
   Google Scholar
• Kessar , R. , Linckelmann , M. ( 2006 ). On blocks of strongly p-solvable groups . Archiv der Mathematik (Basel) 87 : 481 – 487 .
   Web of Science ®Google Scholar
• Knörr , R. ( 1976 ). Blocks, vertices and normal subgroups . Math. Zeit. 148 : 53 – 60 .
   Web of Science ®Google Scholar
• Külshammer , B. , Puig , L. ( 1990 ). Extensions of nilpotent blocks . Invent. Math. 102 : 17 – 71 .
   Web of Science ®Google Scholar
• Külshammer , B. , Robinson , G. R. ( 1986 ). On blocks of finite groups with a certain factorization . Arch. Math. 46 : 97 – 101 .
   Web of Science ®Google Scholar
• Puig , L. Local extensions in endo-permutation modules split: a proof of Dade's Theorem . Publ. Math. Univ. Paris VII 25 : 199 – 205 .
   Google Scholar
• Puig , L. ( 1980 ). Local block theory in p-solvable groups . Proc. Sympos. Pure Math. 37 : 385 – 388 .
   Google Scholar
• Puig , L. ( 1999 ). On the Local Structure of Morita and Richard Equivalences Between Brauer Blocks . Basel : Birkhaüser Verlag .
   Google Scholar
• Serre , J. P. ( 1962 ). Corps Locaux . Paris : Hermann .
   Google Scholar
• Thévenaz , J. ( 1995 ). G-Algebras and Modular Representation Theory . New York : Oxford University Press .
   Google Scholar
• Watanabe , A. ( 1985 ). On generalized decomposition numbers and Fong's reductions . Osaka J. Math. 22 : 393 – 400 .
   Web of Science ®Google Scholar
• Communicated by J. Zhang.
   Google Scholar