ISSN:
1572-9168
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we generalize the concept of (P,l)-transitivity from finite projective planes to arbitrary symmetric designs with λ 〉 1. We define (x ∩ y, x)-transitivity, and show that if a symmetric design D is (x ∩ y, x)-transitive then it is also (x ∩ z, x)-transitive, for all blocks z ≠ x, such that z $$ \supseteq$$ x ∩ y, and x is necessarily a good block. In addition we show that D has the parameters of aP n,q , for some integer n and prime power q, and that if q = 2, x must be a translation block. However, we do give examples of symmetric designs with a proper semi-translation block (i.e. one in which x is not a translation block). Finally, we give a classification of all symmetric designs with λ 〉 1 which contain more than one semi-translation block, and show that there are exactly six types to consider, of which only three can possibly be proper. The results in this paper form part of a Ph.D. thesis submitted by the author to the University of London in 1981.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00147872
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