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Radio and gamma-ray emissions in Active Galactic Nuclei (AGNs) are both related to the presence of relativistic particles in jets. With the advent of the Fermi Large Area Telescope (LAT), and thanks to its large sensitivity up to several GeV, many observational results are changing our understanding of these phenomena. BL Lac objects, which made up only a fraction of the known extragalactic gamma-ray source population before Fermi, have now become the most abundant class. However, since they are relatively weak radio sources, most of them are poorly known as far as their parsec scale structure and multi-wavelength properties are concerned. For this reason, we have selected a complete sample of 42 low redshift BL Lacs (independently of their gamma-ray properties) to study with a multi-wavelength (radio, optical, X-ray, gamma-ray) approach. Here, we present results and images of sources in the sample (most of which have never been observed before), using new VLBA observations ! at 8 and 15 GHz. Beyond this sample of BL Lacs, the population of gamma-ray AGNs has also dramatically enlarged in the Fermi era, permitting us to discuss the presence of a correlation between radio and gamma-ray properties with improved statistical significance. We explore the radio-gamma relation with several hundreds sources and using both simultaneous and archival radio data, thus tackling the impact of time variability. (C) 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.