1995 Fiscal Year Annual Research Report

群環の表現論

Research Project

Project/Area Number	07640011
Research Institution	Gunma University
Principal Investigator	福島博群馬大学, 教育学部, 助教授 (30125869)
Co-Investigator(Kenkyū-buntansha)	西谷泉群馬大学, 教育学部, 助教授 (80261824) 都丸正群馬大学, 医療技術短期大学部, 教授 (70132579) 伊藤隆群馬大学, 教育学部, 助教授 (40193495) 布川護群馬大学, 教育学部, 教授 (00008137) 大竹公一郎群馬大学, 教育学部, 教授 (60134269)
Keywords	群環 / 表現 / 指標 / ブロック / 正規部分群 / 不足群
Research Abstract	有限群Gが、表現論におけるある条件を満すとき、Gはどんな構造を持つか決定せよ。という問題がある。素数pに対して、IBr_p(G)を標数pの代数閉体k上の既約モジュラー指標の集合とするとき、ミヒラ-・奥山は、次の定理を得た。pXβ(1) (pがβ(1)を割らない)任意のβεIBr_p(G)⇔PΔG、ここでPはGのシロ-p部分群とする。これに関連して、q(≠p)素数としたとき、qXβ(1)、任意のβεIBr_p(G)を満す群Gは、どんな群になるかという問題がある。マンツ、ウルフは、p-可解群Gが先の条件を満せば、Gのq-lengthは、2以下であることを証明した。そこで、これらの群の構造を、きっちりと決定することを考え、次の定理を得た。p-可解群Gが先に述べた条件を満せば、Gは、Ar_1n、qm (affine semilinear群の部分群として定義される。)の直積の正規部分群と同型になる。またβεIBr_p (G)に対してp^n\|β(1)(ただしp^nはGのp-シロ-群Pの位数)を満すとき、βをdefect 0の既約指標という。このとき、defect 0の既約指標を持つ群を群論の言葉で述べよ。(これはdefect 0のブロックをもつ群と同値)という問題がある。これに関して、次の定理を得た。Gが奇数位数のp-radical群(P上trivialな既約指数をGに持ち上げた指標(k_p)Gが半単純である。)の時、Gがdefect 0の既約指標を持つ。⇔O_p(G)=1を得た。ここでO_p(G)は、Gのmaximalな正規p-部分群を表す。

Research Products
(33 results)

All Other

All Publications (33 results)

[Publications] H. Fukushima: "On p-radical group and the nilpotency indices of J (kG) II" Osaka J. Math. 33. (1996)
[Publications] H. Fukushima: "On p-radical groups and the nilpotency indices of J (kG)" Osaka J. Math. 31. 773-785 (1994)
[Publications] H. Fukushima: "On the connection between the nilpotency indices of J (kG) and J (kP)" Science Reports of Faculty of Education Gunma University. 43. 35-40 (1995)
[Publications] H. Fukushima: "p-Solvable groups all of whose irreducible modularrep resentations have q'-degrees" 草津セミナー報告集. 7. 1-4 (1995)
[Publications] T. Tomaru: "On Gorenstein surface singularities with fundamental genus P_f≧2 which satisfy some minimality conditions" Pacific J of Math. 170. 271-295 (1995)
[Publications] 小関煕純: "子どもの図形認知と論理" 日数教yearbook 産業図書. 45-57 (1995)
[Publications] UffE HAAGERUP TAKASHI ITOH: "Grothendieck type norms for bilinear forms on C^*-algebras" J. Operator theory. 34. 263-283 (1995)
[Publications] Y. Kotake: "On kβ-Spuces and Some Other Generalized Metric Spaces." 数理解析研究所講究録. 901. 1-7 (1995)
[Publications] Y. Kotake: "On a Class of Spaces with (mod k) Bases." Science Reports of Faculty of Education, Gunma University. 44. (1996)
[Publications] 小竹義朗: "微積分から位相空間へ" BASIC数学. 28. 4-7 (1995)
[Publications] 大竹公一郎: "Morita duality for Grothen dieck categories and its application" Journal of Algebra. 174. 801-822 (1995)
[Publications] 大竹公一郎: "数体系のシナリオ" 群馬大学教育学部紀要. (1996)
[Publications] M. Nunokawa: "On the thory of multivalent functions." Pan American Mathematical Journal. 6 (2) (to appear). (1996)
[Publications] M. Nunokawa 外7名: "Sufficient conditions for starlikeness" Chinese Journal of Mathematics. 24 (1) (to appear). (1996)
[Publications] M. Nunokawa 外2名: "Notes on multivalent functions" Indian Journal of Pure and Applied Mathematics. 26 (8). 797-805 (1995)
[Publications] S. Owa, M. Nunokawa 外2名: "Starlikeness and close-to convexity of certain analytic functions" Far East Journal of Mathematical Science. 2 (2). 143-148 (1995)
[Publications] S. Owa, M. Nunokawa 外1名: "Sufficient conditions for multivalent starlikeness" Annales Polonici Mathematici (Poland). LXII (1). 75-78 (1995)
[Publications] M. Obradovic' and M. Nunokawa: "Some conditions for univalence defined by Ruschweyh's derivative" Yokohama Mathematical Journal. 43 (1). 1-5 (1995)
[Publications] M. Nunokawa 外3名: "Arguments of cartain analytic function" Chinese Journal of Mathematics. 23 (1). 41-48 (1995)
[Publications] S. K. Lee and M. Nunokawa: "On angular estimate of f (z)/z of certain analytic functions" Mathematica Japonica. Accepted on Feb (9) (1997)
[Publications] M. Nunokawa 外2名: "On a criterion of starlikeness" Mathematica Japonica. 44 (3) (to appear). (1996)
[Publications] M. Obradovic and M. Nunokawa: "An application of convolution properties to univalence in the unit disk" Mathematica Japonica. Revised
[Publications] M. Nunokawa: "On some angular estimates of analytic functions" Mathematica Japonica. 41 (2). 447-452 (1995)
[Publications] M. Nunokawa: "On gamma-starlike functions" Science Reports of the Faculty of Education Gunma University. 43. 1-6 (1995)
[Publications] M. Nunokawa and M. K. Aouf: "On certain subclasses of univalent functions with negative coefficients" 京都大学数理解析研究所講究録. 917. 15-39 (1995)
[Publications] M. Nunokawa and M. K. Aouf: "Some applications of fractional calculus operators to certain subclass of analytic functions with negative coefficients" 京都大学数理解析研究所講究録. 917. 40-51 (1995)
[Publications] M. Nunokawa 外2名: "On another easy proof of Owa's result for starlikeness" 京都大学数理解析研究所講究録. 917. 52-54 (1995)
[Publications] N. Koike, M. Nunokawa 外1名: "On meromorphically multivalent functions" 京都大学数理解析研究所講究録. 917. 55-59 (1995)
[Publications] M. Nunokawa 外4名: "On a sufficient condition for the univalency and a theory of non-Caratheodory f" Science Reports of Faculty Education Gunma University. 44. 1-4 (1995)
[Publications] S. K. Lee and M. Nunokawa: "Estimate of the real part of f(z)/z for some classes of univalent functions" Chinese Journal of Mathematics. 23 (3). 287-290 (1995)
[Publications] 著者多数(分担執筆): "小学校算数実践指導全集(第3巻)" 日本教育図書センター, 270 (1995)
[Publications] 西谷泉: "算数であそぼう空間と割合" 岩崎書店, 31 (1994)
[Publications] 西谷泉: "ロゴでアドベンチャー" 岩崎書店, 63 (1995)

1995 Fiscal Year Annual Research Report

群環の表現論

Principal Investigator

福島 博 群馬大学, 教育学部, 助教授 (30125869)

Research Products

[Publications] H. Fukushima: "On p-radical group and the nilpotency indices of J (kG) II" Osaka J. Math. 33. (1996)

[Publications] H. Fukushima: "On p-radical groups and the nilpotency indices of J (kG)" Osaka J. Math. 31. 773-785 (1994)

[Publications] H. Fukushima: "On the connection between the nilpotency indices of J (kG) and J (kP)" Science Reports of Faculty of Education Gunma University. 43. 35-40 (1995)

[Publications] H. Fukushima: "p-Solvable groups all of whose irreducible modularrep resentations have q'-degrees" 草津セミナー報告集. 7. 1-4 (1995)

[Publications] T. Tomaru: "On Gorenstein surface singularities with fundamental genus P_f≧2 which satisfy some minimality conditions" Pacific J of Math. 170. 271-295 (1995)

[Publications] 小関煕純: "子どもの図形認知と論理" 日数教yearbook 産業図書. 45-57 (1995)

[Publications] UffE HAAGERUP TAKASHI ITOH: "Grothendieck type norms for bilinear forms on C^*-algebras" J. Operator theory. 34. 263-283 (1995)

[Publications] Y. Kotake: "On kβ-Spuces and Some Other Generalized Metric Spaces." 数理解析研究所講究録. 901. 1-7 (1995)

[Publications] Y. Kotake: "On a Class of Spaces with (mod k) Bases." Science Reports of Faculty of Education, Gunma University. 44. (1996)

[Publications] 小竹義朗: "微積分から位相空間へ" BASIC数学. 28. 4-7 (1995)

[Publications] 大竹公一郎: "Morita duality for Grothen dieck categories and its application" Journal of Algebra. 174. 801-822 (1995)

[Publications] 大竹公一郎: "数体系のシナリオ" 群馬大学教育学部紀要. (1996)

[Publications] M. Nunokawa: "On the thory of multivalent functions." Pan American Mathematical Journal. 6 (2) (to appear). (1996)

[Publications] M. Nunokawa 外7名: "Sufficient conditions for starlikeness" Chinese Journal of Mathematics. 24 (1) (to appear). (1996)

[Publications] M. Nunokawa 外2名: "Notes on multivalent functions" Indian Journal of Pure and Applied Mathematics. 26 (8). 797-805 (1995)

[Publications] S. Owa, M. Nunokawa 外2名: "Starlikeness and close-to convexity of certain analytic functions" Far East Journal of Mathematical Science. 2 (2). 143-148 (1995)

[Publications] S. Owa, M. Nunokawa 外1名: "Sufficient conditions for multivalent starlikeness" Annales Polonici Mathematici (Poland). LXII (1). 75-78 (1995)

[Publications] M. Obradovic' and M. Nunokawa: "Some conditions for univalence defined by Ruschweyh's derivative" Yokohama Mathematical Journal. 43 (1). 1-5 (1995)

[Publications] M. Nunokawa 外3名: "Arguments of cartain analytic function" Chinese Journal of Mathematics. 23 (1). 41-48 (1995)

[Publications] S. K. Lee and M. Nunokawa: "On angular estimate of f (z)/z of certain analytic functions" Mathematica Japonica. Accepted on Feb (9) (1997)

[Publications] M. Nunokawa 外2名: "On a criterion of starlikeness" Mathematica Japonica. 44 (3) (to appear). (1996)

[Publications] M. Obradovic and M. Nunokawa: "An application of convolution properties to univalence in the unit disk" Mathematica Japonica. Revised

[Publications] M. Nunokawa: "On some angular estimates of analytic functions" Mathematica Japonica. 41 (2). 447-452 (1995)

[Publications] M. Nunokawa: "On gamma-starlike functions" Science Reports of the Faculty of Education Gunma University. 43. 1-6 (1995)

[Publications] M. Nunokawa and M. K. Aouf: "On certain subclasses of univalent functions with negative coefficients" 京都大学数理解析研究所講究録. 917. 15-39 (1995)

[Publications] M. Nunokawa and M. K. Aouf: "Some applications of fractional calculus operators to certain subclass of analytic functions with negative coefficients" 京都大学数理解析研究所講究録. 917. 40-51 (1995)

[Publications] M. Nunokawa 外2名: "On another easy proof of Owa's result for starlikeness" 京都大学数理解析研究所講究録. 917. 52-54 (1995)

[Publications] N. Koike, M. Nunokawa 外1名: "On meromorphically multivalent functions" 京都大学数理解析研究所講究録. 917. 55-59 (1995)

[Publications] M. Nunokawa 外4名: "On a sufficient condition for the univalency and a theory of non-Caratheodory f" Science Reports of Faculty Education Gunma University. 44. 1-4 (1995)

[Publications] S. K. Lee and M. Nunokawa: "Estimate of the real part of f(z)/z for some classes of univalent functions" Chinese Journal of Mathematics. 23 (3). 287-290 (1995)

[Publications] 著者多数(分担執筆): "小学校算数実践指導全集(第3巻)" 日本教育図書センター, 270 (1995)

[Publications] 西谷泉: "算数であそぼう 空間と割合" 岩崎書店, 31 (1994)

[Publications] 西谷泉: "ロゴでアドベンチャー" 岩崎書店, 63 (1995)

福島博群馬大学, 教育学部, 助教授 (30125869)

[Publications] 西谷泉: "算数であそぼう空間と割合" 岩崎書店, 31 (1994)