On the Exponent Conjectures

2020/05/23 by A. E. Antony, Antony, A. E., Viji Z. Thomas +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2005.11513

openalex publication_date 2020/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If p is an odd prime, then we prove that \e(H₂(G,ℤ)) | p \e(G) for p groups of class 7. We prove the same for p groups of class at most p+1 with \e(Z(G))=p. We also prove Schurs conjecture if \e(G/Z(G)) is 2,3 or 6. Furthermore we prove that if G is a solvable group of derived length d and \e(G)=p, then \e(H₂(G,ℤ)) | (\e(G))^d-1. We also show that if G is a finite 2 or 3 generator group of exponent 5, then \e(H₂(G,ℤ)) | (\e(G))².

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