A resolvable Steiner 2-design on v points is 1-rotational if it admits an automorphism of order v-1 leaving its resolution invariant. In this paper we prove the existence of a 1-rotational resolvable S(2,k,v) in the following cases: 1) k=6 and v=5p+1 with p a prime = 1 (mod 12) but \$p \neq 13, 37\$; 2) k=8 and v=7p+1 with p a prime = 1 (mod 8) but \$p \neq 17, 89\$. In each case it follows from a result of Jimbo and Vanstone that there exists a 1-rotational resolvable S(2,k,v) where v=(k-1)P+1 with P an arbitrary product of the associated primes.

Existence results for 1-rotational Resolvable Steiner 2-designs with block size 6 or 8

Abstract

A resolvable Steiner 2-design on v points is 1-rotational if it admits an automorphism of order v-1 leaving its resolution invariant. In this paper we prove the existence of a 1-rotational resolvable S(2,k,v) in the following cases: 1) k=6 and v=5p+1 with p a prime = 1 (mod 12) but \$p \neq 13, 37\$; 2) k=8 and v=7p+1 with p a prime = 1 (mod 8) but \$p \neq 17, 89\$. In each case it follows from a result of Jimbo and Vanstone that there exists a 1-rotational resolvable S(2,k,v) where v=(k-1)P+1 with P an arbitrary product of the associated primes.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1654596`
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