Pro-p groups of positive deficiency

被引：7

作者：

Hillman, Jonathan A. ^{[1
]}

Schmidt, Alexander ^{[2
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] Univ Regensburg, NWF I Math, D-93040 Regensburg, Germany

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2008年 / 40卷

关键词：

D O I：

10.1112/blms/bdn089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma be a finitely presentable pro-p group with a nontrivial, finitely generated closed normal subgroup N of infinite index. Then def (Gamma) <= 1, and if def (Gamma) = 1 then Gamma is a pro-p duality group of dimension 2, N is a free pro-p group and Gamma/N is virtually free. In particular, if the centre of Gamma is nontrivial and def (Gamma) >= 1, then def (Gamma) = 1, cd G <= 2 and Gamma is virtually a direct product F x (p), with F a finitely generated free pro-p group.

引用

页码：1065 / 1069

页数：5

共 14 条

[1] [Anonymous], 2002, ERGEBNISSE MATH IHRE
[2] BAUMSLAG B, 1978, J LOND MATH SOC, V17, P425
[3] A CERTAIN SUBGROUP OF FUNDAMENTAL GROUP
GOTTLIEB, DH
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1965, 87 (04) : 840 - &
[4] Deficiencies of lattices in connected Lie groups
Hillman, JA
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 65 (03) : 393 - 397
[5] HILLMAN JA, 2007, GEOMETRY TOPOLOGY MO, V5
[6] THE SPLITTING OF THE HOCHSCHILD-SERRE SPECTRAL SEQUENCE FOR A PRODUCT OF GROUPS
JANNSEN, U
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1990, 33 (02): : 181 - 183
[7] On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version
Kochloukova, DH
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2006, 204 (03) : 536 - 554
[8] ON CENTER OF GROUP OF A LINK
MURASUGI, K
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (05) : 1052 - &
[9] ON THE PRO-P GOTTLIEB THEOREM
NAKAMURA, H
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1992, 68 (09) : 279 - 282
[10] Neukirch J, 2013, GRUNDLEHR MATH WISS, V323, P1, DOI 10.1007/978-3-540-37889-1

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