A. Azizi

activity

20022022

2

-class field towers of some multiquadratic number fields

19 citations · 99 across the 25 of their papers we have counts for

collaborators

28 papers

math.NT2022

On the exact divisibility by $5$ of the class number of some pure metacyclic fields

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $Γ = Q (5 n)$ be a pure quintic field, where $n$ is a natural number $5^{t h}$ power-free. Let $k = Q (5 n, ζ_{5})$ , with $ζ_{5}$ is a primitive $…

math.NT2022

On some realizable metabelian $5$ -groups

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $G$ be a $5$ -group of maximal class and $γ_{2} (G) = [G, G]$ its derived group. Assume that the abelianization $G / γ_{2} (G)$ is of type $(5, 5)$ and the transfers $V_{H_{1} \to γ_{2} (G)}$ …

math.NT2021

On the capitulation problem of some pure metacyclic fields of degree 20 II

Fouad Elmouhib, Mohemed Talbi, Abdelmalek Azizi

Let $n$ be a $5^{t h}$ power-free naturel number and $k_{0} = Q (ζ_{5})$ be the cyclotomic field generated by a primitive $5^{t h}$ root of unity $ζ_{5}$ . Then $k\,=\,\mathbb{Q}(…

math.NT2020

On the capitulation problem of some pure metacyclic fields of degree 20

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $Γ = Q (5 n)$ be a pure quintic field, where $n$ is a positive integer $5^{t h}$ power-free, $k_{0} = Q (ζ_{5})$ be the cyclotomic field containing a pr…

math.NT2020★ 5 cited

On the Hilbert $2$ -class field towers of some cyclotomic $Z_{2}$ -extensions

Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi

In this paper, we study the length of the $2$ -class field towers and the structure of the Galois groups $Gal (L (K_{n}) / K_{n})$ of the maximal unramified $2$ -extension…

math.NT2020

The generators of $5$ -class group of some fields of degree 20 over $Q$

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $Γ = Q (5 n)$ be a pure quintic field, where $n$ is a positive integer, $5^{t h}$ power-free. Let $k_{0} = Q (ζ_{5})$ be the cyclotomic field containing…

math.NT2020

The 2-rank of the class group of some real cyclic quartic number fields II

Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini

In this paper, we determine the 2-rank of the class group of certain classes of real cyclic quartic number fields. Precisely, we consider the case in which the quadratic subfield i…

math.NT2020

The 2-rank of the class group of some real cyclic quartic number fields

Abdelmalek Azizi, Mohammed Tamimi, Abdelkader Zekhnini

In this paper, we investigate the 2-rank of the class group of some real cyclic quartic number fields. Precisely, we consider the case where the quadratic subfield is Q(\sqrt{l}) w…

math.NT2020★ 19 cited

Units and $2$ -class field towers of some multiquadratic number fields

Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi

In this paper, we investigate the unit groups, the $2$ -class groups, the $2$ -class field towers and the structures of the second $2$ -class groups of some multiquadratic number fiel…

math.NT2020★ 3 cited

$5$ -rank of ambiguous class groups of quintic Kummer extensions

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $k = Q (5 n, ζ_{5})$ , where $n$ is a positive integer, $5^{t h}$ power-free, whose $5 -$ class group is isomorphic to $\mathbb{Z}/5\mathbb{Z}\times\mathbb{Z}/5\ma…

math.NT2020

On some imaginary triquadratic number fields $k$ with $Cl_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini

Let $d$ be a square free integer and $L_{d} := Q (ζ_{8}, d)$ . In the present work we determine all the fields $L_{d}$ such that the $2$ -class group, $Cl_{2} (L_{d})$ , o…

math.NT2019★ 7 cited

On the $2$ -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini

Let $d$ be an odd square-free integer, $m \geq 3$ any integer and $L_{m, d} := Q (ζ_{2^{m}}, d)$ . In this paper, we shall determine all the fields $L_{m, d}$ having an odd…

math.NT2019

5-Class towers of cyclic quartic fields arising from quintic reflection

Abdelmalek Azizi, Yasuhiro Kishi, Daniel C. Mayer +2

Let zeta5 be a primitive fifth root of unity and d<>1 be a quadratic fundamental discriminant not divisible by 5. For the 5-dual cyclic quartic field M=Q((zeta5-zeta5^-1)*d^1/2) of…

math.NT2019★ 2 cited

Principal factors and lattice minima

Siham Aouissi, Abdelmalek Azizi, Moulay Chrif Ismaili +2

Let $k = Q (3 d, ζ_{3})$ , where $d > 1$ is a cube-free positive integer, $k_{0} = Q (ζ_{3})$ be the cyclotomic field containing a primitive cube root o…

math.NT2019★ 7 cited

On the rank of the $2$ -class group of some imaginary triquadratic number fields

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini

Let $d$ be an odd square-free integer and $ζ_{8}$ a primitive $8$ -th root of unity. The purpose of this paper is to investigate the rank of the $2$ -class group of the fields $L_d=\ma…

math.NT2018★ 4 cited

On a Conjecture of Lemmermeyer

Siham Aouissi, Mohamed Talbi, Moulay Chrif Ismaili +1

Let $p \equiv 1 (mod 3)$ be a prime and denote by $ζ_{3}$ a primitive third root of unity. Recently, Lemmermeyer presented a conjecture about $3$ -class groups of pure cubic…

math.NT2018★ 6 cited

Structure of relative genus fields of cubic Kummer extensions

Siham Aouissi, Abdelmalek Azizi, Moulay Chrif Ismaili +2

Let $N = K (3 D)$ be a cubic Kummer extension of the cyclotomic field $K = Q (ζ_{3})$ , containing a primitive cube root of unity $ζ_{3}$ , with cube free integer radicand $D>…

math.NT2018★ 2 cited

Fields $Q (3 d, ζ_{3})$ whose $3$ -class group is of type $(9, 3)$

Siham Aouissi, Mohamed Talbi, Moulay Chrif Ismaili +1

Let $k = Q (3 d, ζ_{3})$ , with $d$ a cube-free positive integer. Let $C_{k, 3}$ be the $3$ -component of the class group of $k$ . By the aid of g…

math.NT2018★ 1 cited

The generators of $3$ -class group of some fields of degree $6$ over $Q$

Siham Aouissi, Moulay Chrif Ismaili, Mohamed Talbi +1

Let $k = Q (3 p, ζ_{3})$ , where $p$ is a prime number such that $p \equiv 1 (mod 9)$ , and let $C_{k, 3}$ be the $3$ -component of the class gr…

math.NT2018★ 4 cited

$3$ -rank of ambiguous class groups of cubic Kummer extensions

Siham Aouissi, Daniel C. Mayer, Moulay Chrif Ismaili +2

Let $k = k_{0} (3 d)$ be a cubic Kummer extension of $k_{0} = Q (ζ_{3})$ with $d > 1$ a cube-free integer and $ζ_{3}$ a primitive third root of unity. Denote by $C_{k, 3}^{(σ)}$ th…

math.NT2016

Capitulation in the absolutely abelian extensions of some number fields II

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

We study the capitulation of $2$ -ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields $k = Q (p q_{1} q_{2}, i)$ , where $i = - 1$ and…

math.NT2015★ 1 cited

Capitulation in the absolutely abelian extensions of some fields $Q (p_{1} p_{2} q, - 1)$

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

We study the capitulation of $2$ -ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $\mathbf{k} =\mathbb{Q}(\sqrt{p_1p_2q}, i)…

math.NT2015★ 12 cited

Structure of $G a l (k_{2}^{(2)} / k)$ for some fields $k = Q (2 p_{1} p_{2}, - 1)$

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

Let $p_{1} \equiv p_{2} \equiv 5 (mod 8)$ be different primes. Put $i = - 1$ and $d = 2 p_{1} p_{2}$ , then the bicyclic biquadratic field $k = Q (d, - 1)$ has an elementary abelian…

math.NT2015★ 5 cited

On the strongly ambiguous classes of $k / Q (- 1)$ where $k = Q (2 p_{1} p_{2}, - 1)$

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

We construct an infinite family of imaginary bicyclic biquadratic number fields $k$ with the 2-ranks of their 2-class groups are $\geq 3$ , whose strongly ambiguous classes of $k/Q(i…

On the exact divisibility by 5 of the class number of some pure metacyclic fields

On some realizable metabelian 5-groups

On the capitulation problem of some pure metacyclic fields of degree 20 II

On the capitulation problem of some pure metacyclic fields of degree 20

On the Hilbert 2-class field towers of some cyclotomic Z2​-extensions

The generators of 5-class group of some fields of degree 20 over Q

The 2-rank of the class group of some real cyclic quartic number fields II

The 2-rank of the class group of some real cyclic quartic number fields

Units and 2-class field towers of some multiquadratic number fields

5-rank of ambiguous class groups of quintic Kummer extensions

On some imaginary triquadratic number fields k with Cl2​(k)≃(2,4) or (2,2,2)

On the 2-class group of some number fields with large degree

5-Class towers of cyclic quartic fields arising from quintic reflection

Principal factors and lattice minima

On the rank of the 2-class group of some imaginary triquadratic number fields

On a Conjecture of Lemmermeyer

Structure of relative genus fields of cubic Kummer extensions

Fields Q(3d​,ζ3​) whose 3-class group is of type (9,3)

The generators of 3-class group of some fields of degree 6 over Q

3-rank of ambiguous class groups of cubic Kummer extensions

Capitulation in the absolutely abelian extensions of some number fields II

Capitulation in the absolutely abelian extensions of some fields Q(p1​p2​q​,−1​)

Structure of Gal(k2(2)​/k) for some fields k=Q(2p1​p2​​,−1​)

On the strongly ambiguous classes of k/Q(−1​) where k=Q(2p1​p2​​,−1​)

On the exact divisibility by $5$ of the class number of some pure metacyclic fields

On some realizable metabelian $5$ -groups

On the Hilbert $2$ -class field towers of some cyclotomic $Z_{2}$ -extensions

The generators of $5$ -class group of some fields of degree 20 over $Q$

Units and $2$ -class field towers of some multiquadratic number fields

$5$ -rank of ambiguous class groups of quintic Kummer extensions

On some imaginary triquadratic number fields $k$ with $Cl_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

On the $2$ -class group of some number fields with large degree

On the rank of the $2$ -class group of some imaginary triquadratic number fields

Fields $Q (3 d, ζ_{3})$ whose $3$ -class group is of type $(9, 3)$

The generators of $3$ -class group of some fields of degree $6$ over $Q$

$3$ -rank of ambiguous class groups of cubic Kummer extensions

Capitulation in the absolutely abelian extensions of some fields $Q (p_{1} p_{2} q, - 1)$

Structure of $G a l (k_{2}^{(2)} / k)$ for some fields $k = Q (2 p_{1} p_{2}, - 1)$

On the strongly ambiguous classes of $k / Q (- 1)$ where $k = Q (2 p_{1} p_{2}, - 1)$