The Automorphism Groups of Steiner Triple Systems Obtained by the Bose Construction
G. J. Lovegrove
DOI: 10.1023/B:JACO.0000011935.37751.c5
Abstract
The automorphism group of the Steiner triple system of order v 
3 (mod 6), obtained from the Bose construction using any Abelian Group G of order 2 s + 1, is determined. The main result is that if G is not isomorphic to Z 3 n \times Z 9 m , n 
0, m 0, the full automorphism group is isomorphic to Hol( G) \times Z 3, where Hol( G) is the Holomorph of G. If G is isomorphic to Z 3 n \times Z 9 m , further automorphisms occur, and these are described in full.
3 (mod 6), obtained from the Bose construction using any Abelian Group G of order 2 s + 1, is determined. The main result is that if G is not isomorphic to Z 3 n \times Z 9 m , n 0, m 0, the full automorphism group is isomorphic to Hol( G) \times Z 3, where Hol( G) is the Holomorph of G. If G is isomorphic to Z 3 n \times Z 9 m , further automorphisms occur, and these are described in full.Pages: 159–170
Keywords: Steiner triple system; Bose construction; automorphism
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References
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2. P.J. Cameron, Combinatorics, Cambridge University Press, Cambridge, England, 1994.
3. T.P. Kirkman, “On a problem in combinations,” Cambridge and Dublin Math. Journal 2 (1847), 191-204.
4. S. MacLane and G. Birkhoff, Algebra, MacMillan, London, 1967.
5. A.P. Street and D.J. Street, Combinatorics of Experimental Design, Clarendon Press, Oxford, 1987.