Finite Groups: Proceedings by A. A. Albert

By A. A. Albert

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545-551. rd al]ulJ . ; [T fJ \ JH ] rt I ; I i* : S rlv' I lw. r8 uorlBauIIIoC ' SOME FINITE GROUPS WITH GEOMETRICAL PROPERTIES by W. Magnus 1. Introduction This is an expository paper. The term geometrical refers to the classical meaning of the word, namely to those properties of a group of transformations which permit the definition of congruence in the corresponding geometry. first attempt at characterizing a group of motions in terms of properties of the group itself seems to be a paper by M.

Math. , vol. )--T59- 164. 15. Collineations and generalized incidence matrices, Trans. Amer. , vol 86 (1957), 284-296. 16. ', vol. ),545-551. rd al]ulJ . ; [T fJ \ JH ] rt I ; I i* : S rlv' I lw. r8 uorlBauIIIoC ' SOME FINITE GROUPS WITH GEOMETRICAL PROPERTIES by W. Magnus 1. Introduction This is an expository paper. The term geometrical refers to the classical meaning of the word, namely to those properties of a group of transformations which permit the definition of congruence in the corresponding geometry.

Conversely, suppose we are given a block design D with b blocks of k letters each, a total of n distinct letters, each letter occurring in r dis- tinct blocks and any pair of distinct letters occurring together in exactly one block. The parameters must satisfy the relations bk=nr r(k-1) = n 1. will satisfy our requirements if transitive on the letters of D and if the subgroup of G fixing Then a group G of automorphisms of D G is doubly all the letters of a block of D is transitive on the remaining letters.

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