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Locally compact (2, 2)-transformation groups

✍ Scribed by Alfonso Di Bartolo; Giovanni Falcone; Karl Strambach

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
215 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

We determine all locally compact imprimitive transformation groups acting sharply 2-transitively on a nontotally disconnected quotient space of blocks inducing on any block a sharply 2-transitive group and satisfying the following condition: if Ξ”1, Ξ”2 are two distinct blocks and Pi, Qi ∈ Ξ”i (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew-field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive locally compact groups.

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