2-transitive symmetric designs

Kantor, William M.

doi:10.1090/S0002-9947-1969-0255422-6

$2$-transitive symmetric designs
HTML articles powered by AMS MathViewer

by William M. Kantor

Trans. Amer. Math. Soc. 146 (1969), 1-28

DOI: https://doi.org/10.1090/S0002-9947-1969-0255422-6

PDF | Request permission

References

N. Burgoyne and P. Fong, The Schur multipliers of the Mathieu groups, Nagoya Math. J. 27 (1966), 733–745. MR 197542
W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
L. Carlitz, A theorem on permutations in a finite field, Proc. Amer. Math. Soc. 11 (1960), 456–459. MR 117223, DOI 10.1090/S0002-9939-1960-0117223-6
Peter Dembowski, Verallgemeinerungen von Transitivitätsklassen endlicher projektiver Ebenen, Math. Z. 69 (1958), 59–89 (German). MR 93732, DOI 10.1007/BF01187393
Peter Dembowski, Kombinatorische Eigenschaften endlicher Inzidenzstrukturen, Math. Z. 75 (1960/61), 256–270 (German). MR 125801, DOI 10.1007/BF01211024

Scharf transitive and scharf fahnentransitive Kollineationsgruppen

149

P. Dembowski, Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Springer-Verlag, Berlin-New York, 1968. MR 0233275
P. Dembowski and A. Wagner, Some characterizations of finite projective spaces, Arch. Math. 11 (1960), 465–469. MR 143095, DOI 10.1007/BF01236976
Daniel Gorenstein and D. R. Hughes, Triply transitive groups in which only the identity fixes four letters, Illinois J. Math. 5 (1961), 486–491. MR 131456
Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215

Combinatorial theory

Note on symmetric block designs with

Über die Kollineationsgruppen einiger Hadamard-Matrizen

D. R. Hughes, Collineations and generalized incidence matrices, Trans. Amer. Math. Soc. 86 (1957), 284–296. MR 93730, DOI 10.1090/S0002-9947-1957-0093730-4
Q. M. Husain, On the totality of the solutions for the symmetrical incomplete block designs: $\lambda =2, k=5$ or $6$, Sankhyā 7 (1945), 204–208. MR 14037
Q. M. Husain, Impossibility of the symmetrical incomplete block design with $\lambda =2$, $k=7$, Sankhyā 7 (1946), 317–322. MR 17249
Noboru It̂o, On a class of doubly, but not triply transitive permutation groups, Arch. Math. (Basel) 18 (1967), 564–570. MR 223441, DOI 10.1007/BF01898859
Noboru It̂o, On permutation groups of prime degree $p$ which contain (at least) two classes of conjugate subgroups of index $p$, Rend. Sem. Mat. Univ. Padova 38 (1967), 287–292. MR 219603
William M. Kantor, Characterizations of finite projective and affine spaces, Canadian J. Math. 21 (1969), 64–75. MR 236040, DOI 10.4153/CJM-1969-007-9
William M. Kantor, Automorphism groups of designs, Math. Z. 109 (1969), 246–252. MR 274306, DOI 10.1007/BF01111409
William M. Kantor, $4$-homogeneous groups, Math. Z. 103 (1968), 67–68. MR 220812, DOI 10.1007/BF01111290
Donald Livingstone and Ascher Wagner, Transitivity of finite permutation groups on unordered sets, Math. Z. 90 (1965), 393–403. MR 186725, DOI 10.1007/BF01112361
Kulendra N. Majumdar, On some theorems in combinatorics relating to incomplete block designs, Ann. Math. Statistics 24 (1953), 377–389. MR 56559, DOI 10.1214/aoms/1177728978
H. B. Mann, Difference sets in elementary Abelian groups, Illinois J. Math. 9 (1965), 212–219. MR 174630
Henry B. Mann, Addition theorems: The addition theorems of group theory and number theory, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1965. MR 0181626
Hirosi Nagao, On multiply transitive groups. I, Nagoya Math. J. 27 (1966), 15–19. MR 200332
T. G. Ostrom and A. Wagner, On projective and affine planes with transitive collineation groups. , Math. Z. 71 (1959), 186–199. MR 0110975, DOI 10.1007/BF01181398

On orthogonal matrices

12

E. T. Parker, On collineations of symmetric designs, Proc. Amer. Math. Soc. 8 (1957), 350–351. MR 86319, DOI 10.1090/S0002-9939-1957-0086319-X
Herbert John Ryser, Combinatorial mathematics, The Carus Mathematical Monographs, No. 14, Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1963. MR 0150048

A combinatorial problem

12

A. Wagner, On collineation groups of projective spaces. I, Math. Z. 76 (1961), 411–426. MR 131813, DOI 10.1007/BF01210987
Asher Wagner, On finite affine line transitive planes, Math. Z. 87 (1965), 1–11. MR 172165, DOI 10.1007/BF01109922
Helmut Wielandt, Finite permutation groups, Academic Press, New York-London, 1964. Translated from the German by R. Bercov. MR 0183775

Kennzeichnung endlicher linearen Gruppen als Permutationsgruppen

11