Structure of the Macdonald groups in one parameter

IF 0.4 3区数学 Q4 MATHEMATICS

Journal of Group Theory Pub Date : 2023-11-08 DOI:10.1515/jgth-2023-0036

Alexander Montoya Ocampo, Fernando Szechtman

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引用次数: 3

Abstract

Abstract Consider the Macdonald groups G ⁢ ( α ) = ⟨ A , B ∣ A [ A , B ] = A α , B [ B , A ] = B α ⟩ G(\alpha)=\langle A,B\mid A^{[A,B]}=A^{\alpha},\,B^{[B,A]}=B^{\alpha}\rangle , α ∈ Z \alpha\in\mathbb{Z} . We fill a gap in Macdonald’s proof that G ⁢ ( α ) G(\alpha) is always nilpotent, and proceed to determine the order, upper and lower central series, nilpotency class, and exponent of G ⁢ ( α ) G(\alpha) .

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麦克唐纳群在一个参数中的结构

考虑麦克唐纳群G≠(α)=⟨A,B∣A [A,B]=A α，B [B,A]=B α⟩G(\alpha)= \langle A,B \mid A^{[A,B]}=A^ {\alpha}，\，B^{[B,A]}=B^ {\alpha}\rangle， α∈Z \alpha\in\mathbb{Z}。我们填补了Macdonald证明G(α) G(\alpha)总是幂零的空白，并进一步确定了G(α) G(\alpha)的阶、上、下中心级数、幂零类和指数。

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来源期刊

Journal of Group Theory 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered. Topics: Group Theory- Representation Theory of Groups- Computational Aspects of Group Theory- Combinatorics and Graph Theory- Algebra and Number Theory