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Dergiler / Konuralp Journal of Mathematics / 2026 / Volume: 14 Issue: 1

Centers, Commutators, and Holomorphs of 2-Groups

Ali Aytekin(PAMUKKALE ÜNİVERSİTESİ)0000-0001-7892-6960
Tunçar Şahan(Aksaray Üniversitesi)0000-0002-6552-4695
Sayfa
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Yayın Tarihi
2026-04-30
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

By connecting actor theory with split extensions and intrinsic algebraic properties, we provide new tools for analyzing symmetries and automorphisms in higher-dimensional algebraic structures.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper explores actor structures in group-groupoids, using the Brown-Spencer theorem to establish actors as universal objects and split extension classifiers.
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Temel Bulgular & Veri:These results extend group-theoretic concepts to 2-groups, bridging algebra and topology.
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Sonuç & Katkı:By connecting actor theory with split extensions and intrinsic algebraic properties, we provide new tools for analyzing symmetries and automorphisms in higher-dimensional algebraic structures.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:2-group · action · actor

Abstract

This paper explores actor structures in group-groupoids, using the Brown-Spencer theorem to establish actors as universal objects and split extension classifiers. We construct the center and commutator subgroup of a group-groupoid, revealing their roles in internal symmetries, and introduce the holomorph as a categorical generalization of the classical holomorph of a group. These results extend group-theoretic concepts to 2-groups, bridging algebra and topology. By connecting actor theory with split extensions and intrinsic algebraic properties, we provide new tools for analyzing symmetries and automorphisms in higher-dimensional algebraic structures.

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Bu Makaleye Atıf Yap

Aytekin, A., Şahan, T. (2026). Centers, Commutators, and Holomorphs of 2-Groups. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521425

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