Abstract: A fastener element has at its male portion a plurality of grooves whose cross sections each form a fractional circle and a plurality of lobes whose cross sections each form a segmental outline of a larger circle, the inner wall of each said groove being connected to the lobe through a wall portion whose cross section assumes a curved line like configuration. The center of the fractional circle is situated nearer to the center of the larger circle than a conjunction of two tangential lines allowed tangentially to contact the larger circle at the intersections of the larger circle and fractional circle. The curved line is connected with the outline of the fractional circle at a point at which a radial line extending from the center of the larger circle is allowed tangentially to contact the fractional circle, or at a point situated farther from the larger circle center than the first-mentioned point.