On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
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Ali Mouhib
Abstract
We study the structure of the Galois group of the maximal unramified 2-extension of some family of number fields of large degree. Especially, we show that for each positive integer n, there exist infinitely many number fields with large degree, for which the defined Galois group is quaternion of order 2n.
(Communicated by Milan Paštéka)
Acknowledgement
The author would like to express its gratitude to King Khalid University, Saudi Arabia for providing administrative and technical support.
The author also thanks the anonymous referee for his/her careful reading of the manuscript and helpful comments.
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© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Prof. RNDr. pavel brunovský, DrSc. passed away ∗dec. 5, 1934 – † dec. 14, 2018
- Ideals and congruences in pseudo-BCH algebras
- Regular double p-algebras
- Distributive nearlattices with a necessity modal operator
- States in generalized probabilistic models: An approach based in algebraic geometry
- Free power-associative n-ary groupoids
- On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
- On the space of generalized theta-series for certain quadratic forms in any number of variables
- Uniqueness and periodicity for meromorphic functions with partial sharing values
- Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
- An inverse boundary problem for fourth-order Schrödinger equations with partial data
- Entropy as an integral operator
- Global behavior of two third order rational difference equations with quadratic terms
- Measures on effect algebras
- Some topological and combinatorial properties preserved by inverse limits
- The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
- Compositions of porouscontinuous functions
- A note on prime divisors of polynomials P(Tk); k ≥ 1
- On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications
- Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations
