The enzyme corresponding to an alpha-galactoside is called alpha-galactosidase; it catalyzes the hydrolysis of substrates that contain α-galactosidic residues, such as glycosphingolipids or glycoproteins.
[1] On the other hand, the enzyme corresponding to beta-galactosides is called beta-galactosidase; it breaks down the disaccharide lactose for instance, into its monosaccharide components, glucose and galactose.
B-galactosidase forms the basis of lac z operon in bacteria which can be used to control gene expression.
B-galactosidase can be used to track the efficiency of bacterial transformation with a recombinant plasmid in a process called Blue/White Color Screening.
[3] In the process called alpha-complementation, one of the fragments (omega) is encoded by a part of a gene of the lac operon that is found in the chromosome of the bacteria, while the other fragment (alpha) is encoded by the other part of the gene that is found in the plasmid.