  Although Compact Groups of galaxies (CGs) have been envisioned as isolated
extremely dense structures in the Universe, it is accepted today that many of
them could be not as isolated as thought. In this work, we study Hickson-like
CGs identified in the Sloan Digital Sky Survey Data Release 16 to analyse these
systems and their galaxies when embedded in different cosmological structures.
To achieve this goal, we identify several cosmological structures where CGs can
reside: Nodes of filaments, Loose Groups, Filaments and cosmic Voids. Our
results indicate that 45 per cent of CGs do not reside in any of these
structures, i.e., they can be considered non-embedded or isolated systems. Most
of the embedded CGs are found inhabiting Loose Groups and Nodes, while there
are almost no CGs residing well inside cosmic Voids. Some physical properties
of CGs vary depending on the environment they inhabit. CGs in Nodes show the
largest velocity dispersions, the brightest absolute magnitude of the
first-ranked galaxy, and the smallest crossing times, while the opposite occurs
in Non-Embedded CGs. When comparing galaxies in all the environments and
galaxies in CGs, CGs show the highest fractions of red/early-type galaxy
members in most of the absolute magnitudes ranges. The variation between
galaxies in CGs inhabiting one or another environment is not as significant as
the differences caused by belonging or not to a CG. Our results suggest a
plausible scenario for galaxy evolution in CGs in which both, large-scale and
local environments play essential roles.
