Genus spectra for split metacyclic groups

A. Weaver

doi:10.1017/S0017089501020067

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An integer n\geq2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus n on which G acts as a group of automorphisms. In this paper, formulae are given for the minimum genus, minimum stable genus and the gap sequence, i.e., the (finite) set of non-genera, for a split metacyclic group of order pq, where p and q are primes. This information completely determines the genus spectrum for such groups.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Sarkar, Siddhartha 2009. On the genus spectrum for p-groups of exponent p and p-groups of maximal class. Journal of Group Theory, Vol. 12, Issue. 1,

Talu, Y. 2011. Abelian $p$-Groups of Symmetries of Surfaces. Taiwanese Journal of Mathematics, Vol. 15, Issue. 3,

O'SULLIVAN, CORMAC and WEAVER, ANTHONY 2011. A DIOPHANTINE FROBENIUS PROBLEM RELATED TO RIEMANN SURFACES. Glasgow Mathematical Journal, Vol. 53, Issue. 3, p. 501.

Schweizer, Andreas 2017. Metacyclic groups as automorphism groups of compact Riemann surfaces. Geometriae Dedicata, Vol. 190, Issue. 1, p. 185.

Carvacho, Mariela Paulhus, Jennifer Tucker, Thomas and Wootton, Aaron 2021. Non-abelian simple groups act with almost all signatures. Journal of Pure and Applied Algebra, Vol. 225, Issue. 4, p. 106552.

Bozlee, Sebastian Lippert, Samuel and Wootton, Aaron 2022. Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics. Vol. 776, Issue. , p. 133.

Sarkar, Siddhartha 2023. Finite symmetries of surfaces of p-groups of co-class 1. Journal of Algebra and Its Applications, Vol. 22, Issue. 06,

Chen, Lei and Lanier, Justin 2024. Constraining mapping class group homomorphisms using finite subgroups. Geometriae Dedicata, Vol. 218, Issue. 5,

Chen, Haimiao and Li, Yang 2024. A new approach to the genus spectra of abelian p-groups. Boletín de la Sociedad Matemática Mexicana, Vol. 30, Issue. 1,

Article contents

Genus spectra for split metacyclic groups

Abstract

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests