Groups with essential dimension one

被引：0

作者：

Chu, Huan ^{[1
]}

Hu, Shou-Jen ^{[2
]}

Kang, Ming-Chang ^{[1
]}

Zhang, Jiping ^{[3
]}

机构：

[1] Natl Taiwan Univ, Dept Math, Taipei 10764, Taiwan

[2] Tamkang Univ, Dept Math, Tamsui, Taiwan

[3] Peking Univ, Dept Math, Beijing 100871, Peoples R China

来源：

ASIAN JOURNAL OF MATHEMATICS | 2008年 / 12卷 / 02期

关键词：

Essential dimension; compression of finite group actions; Galois theory; finite subgroups of SL2(K);

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Denote by ed(K)(G) the essential dimension of G over K. If K is an algebraically closed field with char K = 0, Buhler and Reichstein determine explicitly all finite groups G with ed(K)(G) = 1 [Compositio Math. 106 (1997), Theorem 6.2]. We will prove a generalization of this theorem when K is an arbitrary field.

引用

页码：177 / 191

页数：15

共 11 条

[1]

Berhuy G., 2003, Doc. Math., V8, P279

[2] On the essential dimension of a finite group [J].

Buhler, J ;

Reichstein, Z .

COMPOSITIO MATHEMATICA, 1997, 106 (02) :159-179

[3]

HASHIMOTO K, 2004, GALOIS THEORY MODULA

[4]

Kang MC, 2008, P AM MATH SOC, V136, P809

[5] Compression of finite group actions and covariant dimension [J].

Kraft, Hanspeter ;

Schwarz, Gerald W. .

JOURNAL OF ALGEBRA, 2007, 313 (01) :268-291

[6] PSL(2, 2n)-extensions over F2n [J].

Ledet, A .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2006, 49 (01) :113-116

[7] Finite groups of essential dimension one [J].

Ledet, Arne .

JOURNAL OF ALGEBRA, 2007, 311 (01) :31-37

[8]

MIYAKE K, 1999, ADV STUD CONT MATH P, V1, P137

[9] On the notion of essential dimension for algebraic groups [J].

Reichstein, Z .

TRANSFORMATION GROUPS, 2000, 5 (03) :265-304

[10]

Suzuki M., 1982, Group Theory, VI

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