On the Exponent of the Schur Multiplier

Ammu. E. Antony; Komma Patali; Viji. Z. Thomas

On the Exponent of the Schur Multiplier

Group Theory 2019-09-11 v2

Authors: Ammu. E. Antony , Komma Patali , Viji. Z. Thomas

Abstract

A longstanding problem attributed to I. Schur says that for a finite group $G$ , the exponent of the second homology group $H_2(G, \mathbb{Z})$ divides the exponent of $G$ . In this paper, we prove this conjecture for finite nilpotent groups of odd exponent and of nilpotency class 5, $p$ -central metabelian $p$ groups, and groups considered by L. E . Wilson in \cite{LEW}. Moreover, we improve several bounds given by various authors.

Keywords

schur multiplier exponent of group finite nilpotent group p-central metabelian p-group second homology

Cite

@article{arxiv.1906.06918,
  title  = {On the Exponent of the Schur Multiplier},
  author = {Ammu. E. Antony and Komma Patali and Viji. Z. Thomas},
  journal= {arXiv preprint arXiv:1906.06918},
  year   = {2019}
}

Comments

37 pages. arXiv admin note: text overlap with arXiv:1906.09585

On the Exponent of the Schur Multiplier

Abstract

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