Sylow’s Subgroup Theorem
نویسنده
چکیده
In finite group theory, one of the most influential ideas is the notion of Sylow p-subgroup. It was used to classify many groups of finite order. Despite original intentions to use it with finite group, it was extended to study Lie group, which inspires recent development in p-compact group. Here, we will discuss some aspects of Sylow’s Subgroup Theorem. In particular, the focus is on a finite group with the intention to study simple groups. The main results in this article are the First and the Second Sylow Theorems.
منابع مشابه
Masters Examination in Mathematics
Solution. The 11-Sylow subgroup is Z/11Z; the 5-Sylow subgroup is Z/5Z. By Sylow’s theorem, the 11-Sylow subgroup is normal. Hence, the group is a semi-direct product of its 5 and 11-Sylow subgroups. Since Aut(Z/11Z) = Z/10Z has a unique subgroup of order 5, there are up to isomorphism exactly two groups of order 55: the abelian group Z/55Z and the group with presentation ⟨x, y|x = y = 1, xyx−1...
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