# Some bounds on commutativity degree

Source: [Some bounds on commutativity degree](<https://www.sota2.com/research/paper/68fa4f481e209131ce9620e4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:12:48.492Z

Authors: R. K. Nath, M. K. Yadav

Published: 2011-08-16T10:41:34.000Z

## Abstract

The relative commutativity degree of a subgroup $H$ of a finite group $G$, denoted by $\\Pr(H, G)$, is the probability that an element of $G$ commutes with an element of $H$. In this article we obtain some lower and upper bounds for $\\Pr(H, G)$ and their consequences. We also study an invariance property of $\\Pr(H, G)$ and its generalizations, under isoclinism of pairs of groups.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1108.3202>)

[PDF](<https://arxiv.org/pdf/1108.3202.pdf>)