The Sylow Structure of Scalar Automorphism Groups

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Date
2018-03-22MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2018,05Author
Herfort, Wolfgang
Hofmann, Karl Heinrich
Kramer, Linus
Russo, Francesco G.
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Show full item recordOWP-2018-05
Abstract
For any locally compact abelian periodic group A its automorphism group contains as a subgroup those automorphisms that leave invariant every closed subgroup of A, to be denoted by SAut(A). This subgroup is again a locally compact abelian periodic group in its natural topology and hence allows a decomposition into its p-primary subgroups for p the primes for which topological p-elements in this automorphism subgroup exist. The interplay between the p-primary decomposition of SAut(A) and A can be encoded in a bipartite graph, the mastergraph of A. Properties and applications of this concept are discussed.