  We investigate the NGC 3933 poor galaxy association, that contains NGC 3934,
which is classified as a polar-ring galaxy. The multi-band photometric analysis
of NGC 3934 allows us to investigate the nature of this galaxy and to re-define
the NGC 3933 group members with the aim to characterize the group dynamical
properties and its evolutionary phase. We imaged the group in the far
(FUV,lambda = 1530A) and near (NUV, lambda=2316A) ultraviolet (UV) bands of the
Galaxy Evolution Explorer (GALEX). From the deep optical imaging we determined
the fine structure of NGC 3934. We measured the recession velocity of PGC
213894 which shows that it belongs to the NGC 3933 group. We derived the
spectral energy distribution (SED) from FUV (GALEX) to far-IR emission of the
two brightest members of the group. We compared a grid of smooth particle
hydrodynamical (SPH) chemo-photometric simulations with the SED and the
integrated properties of NGC 3934 and NGC 3933 to devise their possible
formation/evolutionary scenarios. The NGC 3933 group has six bright members: a
core composed of five galaxies, which have Hickson's compact group
characteristics, and a more distant member, PGC 37112. The group velocity
dispersion is relatively low (157+-44 km s-1). The projected mass, from the NUV
photometry, is ~7$\times$10^12 M\odot with a crossing time of 0.04 Hubble
times, suggesting that at least in the center the group is virialized. We do
not find evidence that NGC 3934 is a polar-ring galaxy, as suggested by the
literature, but find that it is a disk galaxy with a prominent dust-lane
structure and a wide type-II shell structure. NGC 3934 is a quite rare example
of a shell galaxy in a likely dense galaxy region. The comparison between
physically motivated SPH simulations with multi-band integrated photometry
suggests that NGC 3934 is the product of a major merger.
