Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.

Keywords:

totally disconnected locally compact groups, scale function, permutation groups, groups acting on graphs totally disconnected locally compact groups, scale function, permutation groups, groups acting on graphs

MSC Classifications:

22D05, 20B07, 20B27, 05C25 show english descriptions General properties and structure of locally compact groups
General theory for infinite groups
Infinite automorphism groups [See also 12F10]
Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 22D05 - General properties and structure of locally compact groups
20B07 - General theory for infinite groups
20B27 - Infinite automorphism groups [See also 12F10]
05C25 - Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

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