Uniscalar p-adic Lie groups

Citation
H. Glockner et Ga. Willis, Uniscalar p-adic Lie groups, FORUM MATH, 13(3), 2001, pp. 413-421
Citations number
14
Categorie Soggetti
Mathematics
Journal title
FORUM MATHEMATICUM
ISSN journal
09337741 → ACNP
Volume
13
Issue
3
Year of publication
2001
Pages
413 - 421
Database
ISI
SICI code
0933-7741(2001)13:3<413:UPLG>2.0.ZU;2-9
Abstract
A totally disconnected, locally compact group G is said to be uniscalar if its scale function SG : G --> N, as defined in [G. A. Willis, The structure of totally disconnected, locally compact groups, Math. Ann. 300 (1994), 34 1-363], is identically I. It is known that G is uniscalar if and only if ev ery element of G normalizes some open, compact subgroup of G. We show that every identity neighbourhood of a compactly generated, uniscalar p-adic Lie group contains an open, compact, normal subgroup. In contrast, uniscalar p -adic Lie groups which are not compactly generated need not possess open, c ompact, normal subgroups.