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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:17:06 +0000Groups with only the identity fixing three letters
https://resolver.caltech.edu/CaltechETD:etd-04142003-092438
Authors: {'items': [{'id': 'Keller-G-E', 'name': {'family': 'Keller', 'given': 'Gordon Ernest'}, 'show_email': 'NO'}]}
Year: 1965
DOI: 10.7907/GVHG-EC49
In this paper, we study finite transitive permutation groups in which only the identity fixes as many as three letters, and in which the subgroup fixing a letter is self normalizing. If G is such a group, the principal results concern the case when G is simple.
In this case, H, the subgroup fixing a letter, is a Frobenius group, MQ, with kernel M and complement Q. If |H| is even we show that either G is doubly transitive or permutation isomorphic to the representation of A[subscript 5] on ten letters.
If |H| is odd we prove that Q is cyclic, M is a p-group, and G has a single class of involutions. Furthermore, the number of groups for which H has a given positive number of regular orbits is finite.https://thesis.library.caltech.edu/id/eprint/1377