Subgroup growth in some pro-p groups

Citation
Y. Barnea et R. Guralnick, Subgroup growth in some pro-p groups, P AM MATH S, 130(3), 2001, pp. 653-659
Citations number
7
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
130
Issue
3
Year of publication
2001
Pages
653 - 659
Database
ISI
SICI code
0002-9939(2001)130:3<653:SGISPG>2.0.ZU;2-0
Abstract
For a group G let a(n)(G) be the number of subgroups of index n and let b(n )(G) be the number of normal subgroups of index n. We show that a(p)k (SL21 ( Fp[[t]])) less than or equal to p(k(k+5)/2) for p >2. If Lambda = Fp[[t]] and p does not divide d or if Lambda = Z(p) and p not equal 2 or d not equ al 2, we show that for all k sufficiently large b(p)k(SLd1 (Lambda)) = b(p k+d 2 -1) (SLd1 (Lambda)). On the other hand if Lambda = Fp[[t]] and p divi des d, then b(n)(SLd1 (Lambda)) is not even bounded as a function of n.