On the size of the Schur multiplier of finite groups

We obtain sharp bounds for the size of the Schur multiplier of finite groups, which improves all existing bounds. Moreover, we also obtain sharp bounds for the second cohomology group \(H^2(G,\mathbb{Z}/p\mathbb{Z})\) of a \(p\)-group with coefficients in \(\mathbb{Z}/p\mathbb{Z}.\)

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Sathasivam Kalithasan, Mavely, Tony N, Thomas, Viji Z
Format: Article
Language:English
Subjects:
Multipliers
Vector spaces
Online Access:Get full text
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Description
Summary:We obtain sharp bounds for the size of the Schur multiplier of finite groups, which improves all existing bounds. Moreover, we also obtain sharp bounds for the second cohomology group \(H^2(G,\mathbb{Z}/p\mathbb{Z})\) of a \(p\)-group with coefficients in \(\mathbb{Z}/p\mathbb{Z}.\)
ISSN:2331-8422