On the unit groups of Burnside rings Dedicated to the memory of Professor Akira Hattori

Tomoyuki YOSHIDA

doi:10.2969/jmsj/04210031

On the unit groups of Burnside rings

Dedicated to the memory of Professor Akira Hattori

Tomoyuki YOSHIDA

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 1 Pages 31-64

DOI https://doi.org/10.2969/jmsj/04210031

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Published: 1990 Received: November 13, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [Ar82] S. Araki, Equivariant stable homotopy theory and idempotents of Burnside rings, Publ. R.I.M.S., Kyoto Univ., 18 (1982), 1193-1212.
[Be70] H. Bender, On groups with abelian Sylow 2-subgroups, Math. Z., 117 (1970), 164-176.
[CR81] C. W. Curtis and I. Reiner, Method of Representation Theory, Wiley-Interscience Publ., New York, 1981.
[Di79] T. tom Dieck, Transformation Groups and Representation Theory, Lecture Notes in Math., 766, Springer, 1979.
[Dr69] A. Dress, A characterization of solvable groups, Math. Z., 110 (1969), 213-217.
[Dr71] A. Dress, Operations in representation rings, in “Proc. Symposia in Pure Math.”. 1971, pp. 39-45.
[Dr73] A. Dress, Contributions to the theory of induced representations, in “Algebraic K-theory II”. Proc. Battle Institute Conf., 1972, Lecture Notes in Math., 342, Springer, 1973, pp. 183-240.
[FT] W. Feit and J. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775-1029.
[G181] D. Gluck, Idempotent formula for the Burnside algebra with applications to the p-subgroup simplicial complex, Illinois J. Math., 25 (1981), 63-67.
[Go68] D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.
[Gr71] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra, 1 (1971), 41-77.
[Ma82] T. Matsuda, On the unit groups of Burnside rings, Japanese J. Math. (New series), 8 (1982), 71-93.
[Ma86] T. Matsuda, A note on the unit groups of the Burnside rings as Burnside ring modules, (to appear).
[MM83] T. Matsuda and T. Miyata, On the unit groups of the Burnside rings of finite groups, J. Math. Soc. Japan, 35 (1983), 345-354.
[ML71] S. MacLane, Categories for the Working Mathematician, Springer, 1971.
[Sa82] H. Sasaki, Green correspondence and transfer theorems of Wielandt type for G-functors, J. Algebra, 79 (1982), 98-120.
[Wa69] J. H. Walter, Finite groups with abelian Sylow 2-subgroups, Ann. of Math., 89 (1969), 405-514.
[Yo78] T. Yoshida, Character-theoretic transfer, J. Algebra, 52 (1978), 1-38.
[Yo80] T. Yoshida, On G-functors I: Transfer theorems for cohomological G-functors, Hokkaido Math. J., 9 (1980), 222-257.
[Yo83] T. Yoshida, Idempotents of Burnside rings and Dress induction theorem, J. Algebra, 80 (1983), 90-105.
[Yo85] T. Yoshida, Idempotents and transfer theorems of Burnside rings, character rings and span rings, in “Algebraic and Topological Theories”. Kinokuniya, Tokyo, 1985, pp. 589-615.

Right : [Ar82] S. Araki, Equivariant stable homotopy theory and idempotents of Burnside rings, Publ. R. I. M. S., Kyoto Univ., 18 (1982), 1193-1212.
[Be70] H. Bender, On groups with abelian Sylow 2-subgroups, Math. Z., 117 (1970), 164-176.
[CR81] C. W. Curtis and I. Reiner, Method of Representation Theory, Wiley-Interscience Publ., New York, 1981.
[Di79] T. tom Dieck, Transformation Groups and Representation Theory, Lecture Notes in Math., 766, Springer, 1979.
[Dr69] A. Dress, A characterization of solvable groups, Math. Z., 110 (1969), 213-217.
[Dr71] A. Dress, Operations in representation rings, in “Proc. Symposia in Pure Math.”, 1971, pp. 39-45.
[Dr73] A. Dress, Contributions to the theory of induced representations, in “Algebraic K-theory II”, Proc. Battle Institute Conf., 1972, Lecture Notes in Math., 342, Springer, 1973, pp. 183-240.
[FT] W. Feit and J. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775-1029.
[G181] D. Gluck, Idempotent formula for the Burnside algebra with applications to the p-subgroup simplicial complex, Illinois J. Math., 25 (1981), 63-67.
[Go68] D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.
[Gr71] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra, 1 (1971), 41-77.
[Ma82] T. Matsuda, On the unit groups of Burnside rings, Japanese J. Math. (New series), 8 (1982), 71-93.
[Ma86] T. Matsuda, A note on the unit groups of the Burnside rings as Burnside ring modules, (to appear).
[MM83] T. Matsuda and T. Miyata, On the unit groups of the Burnside rings of finite groups, J. Math. Soc. Japan, 35 (1983), 345-354.
[ML71] S. MacLane, Categories for the Working Mathematician, Springer, 1971.
[Sa82] H. Sasaki, Green correspondence and transfer theorems of Wielandt type for G-functors, J. Algebra, 79 (1982), 98-120.
[Wa69] J. H. Walter, Finite groups with abelian Sylow 2-subgroups, Ann. of Math., 89 (1969), 405-514.
[Yo78] T. Yoshida, Character-theoretic transfer, J. Algebra, 52 (1978), 1-38.
[Yo80] T. Yoshida, On G-functors I: Transfer theorems for cohomological G-functors, Hokkaido Math. J., 9 (1980), 222-257.
[Yo83] T. Yoshida, Idempotents of Burnside rings and Dress induction theorem, J. Algebra, 80 (1983), 90-105.
[Yo85] T. Yoshida, Idempotents and transfer theorems of Burnside rings, character rings and span rings, in “Algebraic and Topological Theories”, Kinokuniya, Tokyo, 1985, pp. 589-615.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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