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W. Herfort, F. Russo, K.H. Hofmann:
"Locally Compact Near Abelian Groups";
in: "ASC Report 04/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 34.

A locally compact group G is near abelian if it contains
a closed abelian normal subgroup A such that every closed
topologically nitely generated subgroup of G=A is inductively
monothetic and every closed subgroup of A is normal in G. Recent
studies prove that projective limits of nite p-groups (p prime)
are exactly those compact p-groups in which two closed subgroups
commute (that is, are \quasihamiltonian" or \M-groups"). Such
results are extended to locally compact near abelian groups and
their structure is studied. This requires a review of the structure
of locally compact periodic groups and thus of their automorphisms
which leave all closed subgroups invariant. The new de nition of
locally compact near abelian groups necessitates to introuduce inductively monothetic locally compact groups. Their structure is
completely classi ed. The global structure of locally compact near
abelian groups is discussed. At the end of the paper we classify
locally compact quasihamiltonian groups.

Locally Compact Near Abelian Groups"

http://www.asc.tuwien.ac.at/preprint/2014/asc04x2014.pdf