Normal subgroups of doubly transitive automorphism groups of chains
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- by Richard N. Ball and Manfred Droste PDF
- Trans. Amer. Math. Soc. 290 (1985), 647-664 Request permission
Abstract:
We characterize the structure of the normal subgroup lattice of $2$-transitive automorphism groups $A(\Omega )$ of infinite chains $(\Omega , \leqslant )$ by the structure of the Dedekind completion $(\bar \Omega , \leqslant )$ of the chain $(\Omega , \leqslant )$. As a consequence we obtain various group-theoretical results on the normal subgroups of $A(\Omega )$, including that any proper subnormal subgroup of $A(\Omega )$ is indeed normal and contained in a maximal proper normal subgroup of $A(\Omega )$, and that $A(\Omega )$ has precisely $5$ normal subgroups if and only if the coterminality of the chain $(\Omega , \leqslant )$ is countable.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 290 (1985), 647-664
- MSC: Primary 20B27; Secondary 06F15
- DOI: https://doi.org/10.1090/S0002-9947-1985-0792817-5
- MathSciNet review: 792817