#### Vol. 273, No. 1, 2015

 Recent Issues Vol. 301: 1 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
Generators of the Gauss–Picard modular group in three complex dimensions

### BaoHua Xie, JieYan Wang and YuePing Jiang

Vol. 273 (2015), No. 1, 197–211
##### Abstract

In this paper, we will describe a method to obtain the generators system of Gauss–Picard modular group $PU\left(3,1;ℤ\left[i\right]\right)$. More precisely, we will show that $PU\left(3,1;ℤ\left[i\right]\right)$ can be generated by five given transformations: two Heisenberg translations, two Heisenberg rotations and one involution. Indeed, the same method works for the other higher-dimensional Euclidean Picard modular groups.

##### Keywords
complex hyperbolic space, Picard modular groups, generators
##### Mathematical Subject Classification 2010
Primary: 32M05, 22E40
Secondary: 32M15