Dimensions of Zassenhaus filtration subquotients of some pro-$p$-groups

Mináč, Ján; Rogelstad, Michael; Tân, Nguyêñ Duy

doi:10.48550/arxiv.1405.6980

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Bounding M(g T S1

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2018

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“…Let us conserve the notation of [3] and put i n = log p [G : D Remark 5.16. -Calculations of the above type with Poincaré series can be found, for example, in [25] and [26].…”

Section: Bounding M(g T Smentioning

confidence: 99%

On the Invariant Factors of Class Groups in Towers of Number Fields

Hajir¹,

Maire²

2018

Can. j. math.

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Abstract. For a nite abelian p-group A of rank d = dim A pA, let M A ∶= log p A d be its (logarithmic) mean exponent. We study the behavior of the mean exponent of p-class groups in pro-p towers L K of number elds. Via a combination of results from analytic and algebraic number theory, we construct in nite tamely rami ed prop towers in which the mean exponent of p-class groups remains bounded. Several explicit examples are given with p = . Turning to group theory, we introduce an invariant M(G) attached to a nitely generated pro-p group G; when G = Gal(L K), where L is the Hilbert p-class eld tower of a number eld K, M(G) measures the asymptotic behavior of the mean exponent of p-class groups inside L K. We compare and contrast the behavior of this invariant in analytic versus non-analytic groups. We exploit the interplay of group-theoretical and number-theoretical perspectives on this invariant and explore some open questions that arise as a result, which may be of independent interest in group theory.

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“…Let us conserve the notation of [3] and put i n = log p [G : D Remark 5.16. -Calculations of the above type with Poincaré series can be found, for example, in [25] and [26].…”

Section: Bounding M(g T Smentioning

confidence: 99%

On the Invariant Factors of Class Groups in Towers of Number Fields

Hajir¹,

Maire²

2018

Can. j. math.

View full text Add to dashboard Cite

show abstract

Dimensions of Zassenhaus filtration subquotients of some pro-$p$-groups

Cited by 1 publication

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On the Invariant Factors of Class Groups in Towers of Number Fields

On the Invariant Factors of Class Groups in Towers of Number Fields

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