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Block‐transitive triple systems with sporadic or alternating socle.
- Source :
-
Journal of Combinatorial Designs . Sep2024, Vol. 32 Issue 9, p521-531. 11p. - Publication Year :
- 2024
-
Abstract
- This paper is a contribution to the classification of all pairs (T,G) $({\mathscr{T}},G)$, where T ${\mathscr{T}}$ is a triple system and G $G$ is a block‐transitive but not flag‐transitive automorphism group of T ${\mathscr{T}}$. We prove that if the socle of G $G$ is a sporadic or alternating group, then one of the following holds: (i)T ${\mathscr{T}}$ is a TS(10,2) $TS(10,2)$ and G≅A5 $G\cong {A}_{5}$;(ii)T ${\mathscr{T}}$ is a TS(10,4) $TS(10,4)$ and G≅S5 $G\cong {S}_{5}$;(iii)T ${\mathscr{T}}$ is a TS(55,28) $TS(55,28)$ and G≅A11 $G\cong {A}_{11}$ or S11 ${S}_{11}$;(iv)T ${\mathscr{T}}$ is a TS(55,λ) $TS(55,\lambda)$ with λ∈{4,8,16} $\lambda \in \{4,8,16\}$ and G≅M11 $G\cong {M}_{11}$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTOMORPHISM groups
*STEINER systems
Subjects
Details
- Language :
- English
- ISSN :
- 10638539
- Volume :
- 32
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Designs
- Publication Type :
- Academic Journal
- Accession number :
- 178396295
- Full Text :
- https://doi.org/10.1002/jcd.21945