Definitions of finite
Paul Howard, Mary Yorke (1989)
Fundamenta Mathematicae
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Paul Howard, Mary Yorke (1989)
Fundamenta Mathematicae
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John Truss (1974)
Fundamenta Mathematicae
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Zhu, Zuo-Tong, Huang Zhenyu (1999)
Czechoslovak Mathematical Journal
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We give some necessary and sufficient conditions for transitive -permutation groups to be -transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive -permutation groups to be normal-valued.
J. Truss (1978)
Fundamenta Mathematicae
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Urlich Felgner, Thomas Jech (1973)
Fundamenta Mathematicae
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Paul Howard, Herman Rubin, Jean Rubin (1973)
Fundamenta Mathematicae
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Paul Howard, Jean Rubin (1977)
Fundamenta Mathematicae
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Horst Herrlich, Paul Howard, Eleftherios Tachtsis (2012)
Commentationes Mathematicae Universitatis Carolinae
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A Russell set is a set which can be written as the union of a countable pairwise disjoint set of pairs no infinite subset of which has a choice function and a Russell cardinal is the cardinal number of a Russell set. We show that if a Russell cardinal has a ternary partition (see Section 1, Definition 2) then the Russell cardinal fails to have such a partition. In fact, we prove that if a ZF-model contains a Russell set, then it contains Russell sets with ternary partitions as well...
Pedro Lopes (2009)
Open Mathematics
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In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive...