Abstract
We study (s, k, λ1, λ2)-translation divisible designs with λ1≠0 in the singular and semi-regular case. Precisely, we describe singular (s, k, λ1, λ2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, λ1, λ2)-TDD's (and, more general, for the case λ2>λ1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case.
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Schulz, RH., Spera, A.G. Divisible designs and groups. Geom Dedicata 44, 147–157 (1992). https://doi.org/10.1007/BF00182946
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DOI: https://doi.org/10.1007/BF00182946