Cardinal invariants distinguishing permutation groups

Taras Banakh; Heike Mildenberger

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arXiv · 1506.08969

Cardinal invariants distinguishing permutation groups

Taras Banakh·Heike Mildenberger

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Abstract

We prove that for infinite cardinals $\kappa<\lambda$ the alternating group $Alt(\lambda)$ (of even permutations) of $\lambda$ is not embeddable into the symmetric group $Sym(\kappa)$ (of all permutations) of $\kappa$. To prove this fact we introduce and study several monotone cardinal group invariants which take value $\kappa$ on the groups $Alt(\kappa)$ and $Sym(\kappa)$.

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Taras Banakh, Heike Mildenberger. 2015-06-30. Cardinal invariants distinguishing permutation groups. https://arxiv.org/abs/1506.08969

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