DOUBLE COSET SEPARABILITY OF ABELIAN SUBGROUPS OF HYPERBOLIC n-ORBIFOLD GROUPS

被引：0

作者：

Hamilton, Emily ^{[1
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 06期

关键词：

SURFACE GROUPS; MANIFOLDS;

D O I：

10.1090/proc/12904

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subset X of a group G is said to be separable if it is closed in the profinite topology. Let M = H-n/Gamma be a closed hyperbolic orbifold of dimension n >= 2. We show that if H and K are abelian subgroups of Gamma and g is an element of Gamma, then the double coset HgK is separable in Gamma. We generalize this result to cocompact lattices in linear, semisimple Lie groups of (real) rank one.

引用

页码：2327 / 2336

页数：10

共 15 条

[1]

Agol I, 2013, DOC MATH, V18, P1045

[2]

ALPERIN RC, 1987, ENSEIGNEMENT MATH, V33, P269

[3] GROUPS OF INTEGRAL-REPRESENTATION TYPE [J].

BASS, H .

PACIFIC JOURNAL OF MATHEMATICS, 1980, 86 (01) :15-51

[4] Hyperplane sections in arithmetic hyperbolic manifolds [J].

Bergeron, Nicolas ;

Haglund, Frederic ;

Wise, Daniel T. .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2011, 83 :431-448

[5]

Chen S. S., 1974, Contributions to Analysis A Collection of Papers Dedicated to Lipman Bers, P49, DOI 10.1016/B978-0-12-044850-0.50013-7

[6]

Fisher David, 2007, MATH SCI RES I PUBL, V54, P45, DOI [10.1017/CBO9780511755187.003, DOI 10.1017/CB09780511755187.003]

[7] Finite quotients of rings and applications to subgroup separability of linear groups [J].

Hamilton, E .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (05) :1995-2006

[8] Abelian subgroup separability of Haken 3-manifolds and closed hyperbolic n-orbifolds [J].

Hamilton, E .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2001, 83 :626-646

[9] Separability of double cosets and conjugacy classes in 3-manifold groups [J].

Hamilton, Emily ;

Wilton, Henry ;

Zalesskii, Pavel A. .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2013, 87 :269-288

[10]

HEMPEL J, 1987, ANN MATH STUD, P379

← 1 2 →