On the Automorphism Group of a Free Pro‐ l  Meta‐abelian Group and an Application to Galois Representations | Zendy

Tsunogai Hiroshi | Zendy

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On the Automorphism Group of a Free Pro‐ l Meta‐abelian Group and an Application to Galois Representations

Author(s) -

Tsunogai Hiroshi

Publication year - 1995

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19951710119

Subject(s) - mathematics , quotient , outer automorphism group , conjugacy class , order (exchange) , automorphism , galois module , rank (graph theory) , abelian group , inner automorphism , quotient group , group (periodic table) , pure mathematics , combinatorics , cyclic group , automorphism group , chemistry , organic chemistry , finance , economics

In § l of this article, we study group‐theoretical properties of some automorphism group Ψ * of the meta‐abelian quotient § of a free pro‐ l group § of rank two, and show that the conjugacy class of some element of order two of Ψ * is not determined by the action induced on the abelian quotient § of § in the case of § = 2. In § 2 we apply the results to the outer Galois representation § attached to the curve C deleted one point from an elliptic curve E , and give an example that § c does not factor through the l ‐adic representation attached to E .

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