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Displaying similar documents to “Steinitz classes of tamely ramified nonabelian extensions of odd prime power order”

Compactification-like extensions

M. R. Koushesh

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Let X be a space. A space Y is called an extension of X if Y contains X as a dense subspace. For an extension Y of X the subspace Y∖X of Y is called the remainder of Y. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X pointwise. For two (equivalence classes of) extensions Y and Y' of X let Y ≤ Y' if there is a continuous mapping of Y' into Y which fixes X pointwise. Let 𝓟 be a topological property. An extension Y of X is called a 𝓟-extension...

Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients

Yoko Inoue, Kaori Ota (2015)

Acta Arithmetica

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We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies q p - 1 ≡ 1 ( m o d p n + 1 ) , and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree...