Discount stock brokers now account for more than 4 percent of all retail share volume and "are one of the most profitable and rapidly growing segments" of the nation's securities industry, according to a government report issued recently.

At least 55 brokerage firms were featuring discounted commission rates throughout the nation at the end of last year, and only 8 of the firms had been in business for a decade, the Securities and Exchange Commission said.

Typically, the discount firms offer individuals reduced commission rates on investment transactions without the detailed research and personal attention provided a major national and retail brokerage offices.

In addition, discount brokers rely on "mass media print advertising rather than personal selling...a marketing innovation consistent with other aspects of their business strategy," the SEC's economic and policy research office noted.

Twenty of the 55 firms in business last year have entered the business since May 1975, when the historic practice of fixed commission rates throughout the Wall Street community was abolished.

During 1978, commission revenues for 16 established discount brokers soared 80 percent while pre-tax profits climbed 300 percent. In contrast, commission revenues for New York Stock Exchange member firms rose 35 percent and pre-tax profits advanced 65 percent.

Overall, profits of the securities industry rose substantially last year for NYSE-member firms but declined for regional and over-the-counter traders, the SEC said.

At the same time, brokerage commission rates last year remained relatively stable with a slight, temporary increase occurring during periods of heavy volume.

Concentration in the business "has increased markedly" since fixed commissions were outlawed, but the SEC said this only continued a trend which began well before what Wall Street calls "May Day."