The structure of the lattice of subgroups of the symmetric group s5
Abstract
In this paper we determine all the subgroups of the symmetric group S5 explicitly by applying Lagrange’s theorem, Sylow’s theorem. We give the diagram of the lattice of subgroups of S5. We also study some lattice theoretic properties of the lattice of subgroups of Sn, when n 5.
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- Conjugacy classes of groups of prime order in $\mathrm{PGL}_{k+1}(\mathbb{C})$ ↗
Andrea Marinatto · arXiv (Cornell University) · 2020
Let $\mathbb{C}$ be the field of complex numbers. Let $k$ be natural number with $k \geq 2$ and let $p$ be a rational prime. In this paper we count the number of conjugacy classes of admissible cyclic subgroups of $\mathrm{PGL}_{k+1}(\mathbb{C})$ of order $p$, where with admissible we intend those finite subgroups that can be contained in the automorphism group of…
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