Pseudo Sylow numbers
Group Theory
2018-12-24 v1
Abstract
One part of Sylow's famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer occurs as the number of Sylow p-subgroups of some finite group. While Hall's proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.
Keywords
Cite
@article{arxiv.1812.08988,
title = {Pseudo Sylow numbers},
author = {Benjamin Sambale},
journal= {arXiv preprint arXiv:1812.08988},
year = {2018}
}
Comments
6 pages, expository, to appear in Amer. Math. Monthly