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arXiv · 1812.08988

Pseudo Sylow numbers

Benjamin Sambale
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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 $n\equiv 1\pmod{p}$ 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.

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Benjamin Sambale. 2018-12-21. Pseudo Sylow numbers. https://doi.org/10.1080/00029890.2019.1528825

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