The Groups G2(2m) and 3D4(23m) as Automorphism Groups of Regular Polytopes of Rank 3, 4, and 5

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2026-08-28 DOI:10.1007/s10469-026-09844-2

R. I. Gvozdev, Ya. N. Nuzhin

引用次数: 0

Abstract

We prove that G₂(2^m) and ³D₄(2^3m) are automorphism groups of regular polytopes of rank n = 4, 5, except for the group ³D₄(2^3m) when n = 5 and m is a power of 3. The minimal number of generating conjugate involutions whose product equals 1 is found, and the existence of new regular polytopes of rank 3 with these automorphism groups is established.

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群G2（2m）和3D4（23m）为3、4、5阶正多面体的自同构群

我们证明了G2（2m）和3D4（23m）是秩为n = 4,5的正多面体的自同构群，除了当n = 5且m为3的幂时3D4（23m）群。得到了乘积为1的共轭对合的最小个数，并证明了具有这些自同构群的3阶新正则多面体的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.