Pentactions and action representability in the category of reduced groups with action-Reference-Cited by-同舟云学术

Pentactions and action representability in the category of reduced groups with action

Published:2022-11-30 Issue:2 Volume:30 Page:195-209
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Datuashvili Tamar¹^ORCID,Şahan Tunçar²^ORCID

Affiliation:

1. A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University , 2 Merab Kostava II Lane , Tbilisi 0193 , Georgia

2. Department of Mathematics , Aksaray University , Aksaray , Türkiye

Abstract

Abstract A notion of pentaction of any object in the category 𝐫𝐆𝐫 ∙

{\mathbf{rGr}^{\bullet}}

of reduced groups with action is introduced. The operations are defined in the set 𝖯𝖾𝗇𝗍𝖺𝖼𝗍 ⁢ ( A )

{\mathsf{Pentact}(A)}

of pentactions of an object A of 𝐫𝐆𝐫 ∙

{\mathbf{rGr}^{\bullet}}

. It is proved that if an object A is perfect with zero weak stabilizer in the sense defined in this paper, then 𝖯𝖾𝗇𝗍𝖺𝖼𝗍 ⁢ ( A )

{\mathsf{Pentact}(A)}

is an object of 𝐫𝐆𝐫 ∙

{\mathbf{rGr}^{\bullet}}

, it has a derived action on A, the object A is action representable and 𝖯𝖾𝗇𝗍𝖺𝖼𝗍 ⁢ ( A )

{\mathsf{Pentact}(A)}

represents all actions on A.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2022-2205/pdf

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