Abstract
From now on we fix once and for all a prime number p.
Let G be any abstract group. A p-valuation ω on G is a real valued function
which, with the convention that ω(1)=∞, satisfies
-
(a)
\(\omega(g) > \frac{1}{p-1}\),
-
(b)
ω(g −1 h)≥min (ω(g),ω(h)),
-
(c)
ω([g,h])≥ω(g)+ω(h),
-
(d)
ω(g p)=ω(g)+1
for any g,h∈G. Here the commutator is normalized to be [g,h]=ghg −1 h −1; as usual, for any two subsets A,B⊆G we will write [A,B] for the subgroup of G generated by the set of commutators {[g,h]:g∈A,h∈B}.
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© 2011 Springer-Verlag Berlin Heidelberg
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Schneider, P. (2011). p-Valued Pro-p-Groups. In: p-Adic Lie Groups. Grundlehren der mathematischen Wissenschaften, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21147-8_5
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DOI: https://doi.org/10.1007/978-3-642-21147-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21146-1
Online ISBN: 978-3-642-21147-8
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