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Locally compact (2, 2)‐transformation groups
Author(s) -
Di Bartolo Alfonso,
Falcone Giovanni,
Strambach Karl
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910244
Subject(s) - mathematics , locally compact space , locally compact group , totally disconnected space , group (periodic table) , combinatorics , quotient , affine transformation , compact group , topological group , pure mathematics , automorphism , block (permutation group theory) , topology (electrical circuits) , lie group , chemistry , organic chemistry
We determine all locally compact imprimitive transformation groups acting sharply 2‐transitively on a non‐totally disconnected quotient space of blocks inducing on any block a sharply 2‐transitive group and satisfying the following condition: if Δ 1 , Δ 2 are two distinct blocks and P i , Q i ∈ Δ i ( i = 1, 2), then there is just one element in the inertia subgroup which maps P i onto Q i . 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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)