Some Characterizations of a Normal Subgroup of a Group

2012/02/25 by Vipul Kakkar, Kakkar, Vipul, Ravi Prakash Shukla +2
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1202.5626

openalex publication_date 2012/02/25 · arxiv created 2012/03/12 · arxiv updated 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of [5], which avoids the use of the classification of finite simple groups

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