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 Hicksons 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 Modot 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.
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