On distinguishing quotients of symmetric groups

John Truss; Saharon Shelah

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arXiv · math/9805147

On distinguishing quotients of symmetric groups

John Truss·Saharon Shelah

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Abstract

A study is carried out of the elementary theory of quotients of symmetric groups in a similar spirit to [Sh:24]. Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S(mu) on an infinite cardinal mu are all of the form S_kappa(mu)= the subgroup consisting of elements whose support has cardinality 2^{aleph_0}, cf(kappa) <= 2^{aleph_0}< kappa, aleph_0< kappa < 2^{aleph_0}, and kappa = aleph_0, we make a further analysis of the first order theory of S_lambda(mu)/S_kappa(mu), introducing many-sorted second order structures N^2_{kappa lambda mu}, all of whose sorts have cardinality at most 2^{aleph_0} .

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BibTeX RIS

John Truss, Saharon Shelah. 1998-05-15. On distinguishing quotients of symmetric groups. https://arxiv.org/abs/math/9805147

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