The Double Transitivity of a Class of Permutation Groups
1965 ◽
Vol 17
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pp. 480-493
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Certain finite groups H do not occur as a regular subgroup of a uniprimitive (primitive but not doubly transitive) group G. If such a group H occurs as a regular subgroup of a primitive group G, it follows that G is doubly transitive. Such groups H are called B-groups (8) since the first example was given by Burnside (1, p. 343), who showed that a cyclic p-group of order greater than p has this property (and is therefore a B-group in our terminology).Burnside conjectured that all abelian groups are B-groups. A class of counterexamples to this conjecture due to W. A. Manning was given by Dorothy Manning in 1936 (3).
1988 ◽
Vol 103
(2)
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pp. 213-238
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1995 ◽
Vol 44
(2)
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pp. 395-402
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2020 ◽
Vol 0
(0)
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Keyword(s):
2018 ◽
Vol 17
(08)
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pp. 1850146
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1996 ◽
Vol 39
(3)
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pp. 294-307
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2019 ◽
Vol 168
(3)
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pp. 613-633
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Keyword(s):
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