Transitive substitution groups containing regular subgroups of lower degree.
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Transitive substitution groups containing regular subgroups of lower degree.

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Published in [n.p .
Written in English


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Edition Notes

(Reprinted from The American Journal of Mathematics, Vol. 50, No. 2, p. 231-242)

The Physical Object
Pagination[12 p.]
Number of Pages12
ID Numbers
Open LibraryOL15343960M

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A triply transitive group of degree p+2 is completely determined by any one of its maximal doubly transitive subgroups of degree p+1 in the sense that only one triply transitive group of degree p+2 can involve a given group of degree p +1 as the subgroup composed of all its substitutions . Dissertation: Transitive Substitution Groups Containing Regular Subgroups of Lower Degree Mathematics Subject Classification: 20—Group theory and generalizations Advisor: George Abram Miller. Transitive Subgroups of S T Name(s) |G| Parity |C S 10 (G)| Subfields Other Representations Resolvents 1: C(10)=5[x]2: 10 = 2 5. Substitution groups of degree n and class n1 are composite. Group of isomorphisms of a transitive substitution group. Groups involving no more than one noncyclic Sylow subgroup. PART II. _ Change of variables _ Group containing the group for the 28 bitangents. .

Transitive Subgroups of S T Name(s) |G| Parity |C S 12 (G)| Subfields Other Representations Resolvents 1: C(4)[x]C(3) 12 = 2 2 Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share . ON MULTIPLY TRANSITIVE GROUPS* BY W. A. MANNING The properties of primiti-e groups that contain transitive subgroups of lower degree were first investigated by Jordan.-)- In the Traité des Substitutions he proved that if a primitive group of degree n contains a circular substitution. sense that only one triply transitive group of degree p +2 can involve a given group of degree p + 1 as the subgroup composed of all its substitutions which omit a given letter. In particular, the number of the triply transitive substitution groups of degree p+2 can certainly not exceed the number of the doubly transitive groups of degree p+1.

  5. C. HERING, On linear groups which contain an irreducible subgroup of prime order, presented at the International Conference on Projective Planes, Washington State University, , pp. 6. C. HERING, Transitive linear groups and linear groups which contain irreducible subgroups of prime order. Geometriae Dedicata 2 (), 7. This collection contains research notes and drafts for Johnston's PhD. thesis Transitive Substitution Groups Containing Regular Subgroups of Lower Degree. Physical Location Materials may be stored off-site, and may require additional retrieval time. Doubly transitive groups are Frobenius groups, their degrees are prime powers. These groups have been investigated frequently. The sharply simply transitive groups are the regular groups. They have no special structure as every abstract group are faithfully represented as a regular permutation group. A primitive group that contains a. The Transitive Property for four things is illustrated in the below figure. Substitution Property: If two geometric objects (segments, angles, triangles, or whatever) are congruent and you have a statement involving one of them, you can pull the switcheroo and replace the one with the other.(Note that you will not be able to find the term “switcheroo” in your geometry glossary.).