On a conjecture of Lemmermeyer

Aouissi, Siham; Talbi, Mohamed; Ismaili, Moulay Chrif; Azizi, Abdelmalek

doi:10.1142/s1793042120500748

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Cited by 3 publications

(2 citation statements)

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“…Thus, if p ≡ 4, 7 mod 9 and 3 p 3 = 1, Theorem 1.1 implies that q = 3. This confirms a conjecture made in [ATIA20].…”

Section: Introductionsupporting

confidence: 92%

The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure

Li,

Zhang

2020

Preprint

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“…Thus, if p ≡ 4, 7 mod 9 and 3 p 3 = 1, Theorem 1.1 implies that q = 3. This confirms a conjecture made in [ATIA20].…”

Section: Introductionsupporting

confidence: 92%

The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure

Li,

Zhang

2020

Preprint

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“…Aoshima and coworkers used a heteropolyacid with the Keggin structure as a catalyst for the polymerization of THF to obtain PTMG in water without the hydrolysis step. 20 This one-step process appeared to be effective for the production of low-molecular-weight PTMG in a reasonable yield, although a large amount of the catalyst was required. Despite the development of numerous catalysts for the synthesis of PTMG or PTMG derivatives, the design of an efficient and economical catalyst still remains a challenging issue.…”

Section: Introductionmentioning

confidence: 98%

Highly efficient ring‐opening polymerization of tetrahydrofuran by anhydrous ferric chloride

Yang

Yoon

Park

et al. 2019

J of Applied Polymer Sci

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Poly(tetramethylene ether glycol) (PTMG), widely used as a precursor in the fabrication of commodity polymers, is typically produced byacid‐catalyzed polymerization of tetrahydrofuran (THF). Herein, we report a detailed investigation of the cationic ring‐opening polymerization of THF catalyzed by ferric chloride (FeCl3), which can be considered as a strong Lewisacid. The polymerization reactions were performed in the presence of acetic anhydride at 20°C with FeCl3, which readily produced poly(tetramethylene ether glycol diester) (PTMG_DE). A maximum yield of 79.2% was obtained within 30 min using a FeCl3 to acetic anhydride molar ratio of 5:4. The resulting polymers generally exhibited low molecular weights and a narrow polydispersity index and could be easily converted into PTMG using aqueous NaOH. In contrast with the FeCl3‐acetic anhydride system, other iron‐based catalysts such as FeCl2 and FeCl3·6H2O did not show any noticeable activity in the polymerization of THF. The proposed mechanism involves initiation of the acetyl cation generated by FeCl3, propagation by nucleophilic addition of THF, and termination by the acetate anion, accounting for the high activity of the FeCl3 catalyst for THF polymerization. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47999.

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The 3-class groups of $$\mathbb {Q}(\root 3 \of {p})$$ and its normal closure

Zhang

2021

Math. Z.

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On a conjecture of Lemmermeyer

Cited by 3 publications

References 13 publications

The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure

The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure

Highly efficient ring‐opening polymerization of tetrahydrofuran by anhydrous ferric chloride

The 3-class groups of $$\mathbb {Q}(\root 3 \of {p})$$ and its normal closure

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