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The term FGK star designates a star that is either an F-type star, a G-type star, or a K-type star. For main sequence stars fitting the category, there is some similarity to their stellar structure as opposed to earlier types or M dwarfs, and the Sun falls within this category, making it plausible that life would be found in such a system. Some star surveys cover this set of classes, among them some looking for biosignatures.
Also, the term GKM star has been used for G, K, and M-type stars, i.e., stars of roughly solar mass and less.