There is a rich potential for police-community problems in the Groveton area of Fairfax County just below Alexandria.

Slashing through the area like a bar sinister is Route 1, which is dotted with beer bars and one-night motels beckoning the restless looking for a good time -- or maybe a night's cash receipts. Just beyond the harsh glare of Route 1 are small black, white and racially mixed neighborhoods of cottages, apartments and trailers. Some of the residents live on the economic and emotional margins, and sometimes they fall off.

One measure of the social dislocations in the area (or the aggressiveness of the police, if you prefer) is the number of people who are arrested for public drunkenness. In 1968, the total was 1,136, or almost twice as many as in the second-ranked district in the country.

But the angry atmosphere in Groveton goes far beyond what might be considered an expectable level of police-community friction.

How bad police-community relations are can be gauged by considering two pieces of evidence. One is a poem stapled to the bulletin board of the Groveton station. It says, in part: I am a policeman, You call me to chase the kids off your lawn, then you call me a bully, You call me when your husband beats you, but you shout pig when he's handcuffed . . . Now you have spat upon me the worst insult . . . You've disturbed forever my eternal rest. You've left unpunished my murder, Don't call me anymore.

The counterpoint is provided by attorney James M. Lowe, who often represents people arrested in the Groveton area: "Groveton is a dumping ground for officers inclined to brutality and citizen abuse."

There is, of course, nothing unique about a community like Groveton or the fact that it has terrible relations with its police. What is unique is how the community took what had been a Babel of grumblings and brought them together in a chorus of articulate grievances that, for the first time, were not only heard but at least partially heeded.

It all began last December when residents of the black community of Gum Springs formed an organization called Fairfax County Concerned Citizens for Better Law Enforcement and Improved Community Relations. The impetus was the deaths of three blacks at the Fairfax Jail within a matter of months.

In February, they decided to hold "public hearings" on the case of 28-year-old Donald Ferguson, one of their neighbors, who died of kidney failure at Western State Hospital after he had gone into alcohol withdrawal at the Fairfax Jail and then had been shackled head to foot and forced to lay in his food and urine. There were suspicions -- totally unfounded, as it turned out -- that Ferguson had been beaten by the police. The hearings quickly expanded into a lengthy catalogue of horror stories involving allegations of brutality concerning the Groveton police.

The police have pointed out, with justification, that the hearings were controlled entirely by the organizers and told only one side of the story. But still the police were there listening. And they couldn't help noticing that the members of the public hearing board included such public officials as Rep. Herbert E. Harris II (D-Va.) and State Sen. Joseph V. Gartlan Jr. (D-Fairfax), both of whose districts include the Groveton area.

Within weeks, there began a series of changes within the ordinarily slow-moving Fairfax police department. First, Police Chief Richard A. King announced he was setting up police advisory boards -- nothing like the police-monitoring citizens' councils the organizers of the hearings wanted, but at least a small opening in what has been an effectively closed system. A third supervisor was assigned to Groveton so there would always be a top officer on duty to oversee police conduct with suspects at the station. Roll-call training at the station included a visit from a psychologist who "generally sensitizes officers to roles they take in the community" -- an idea that might have been derisively dismissed a couple of years ago. And only a couple of weeks ago, King announced that foot patrols would be introduced countywide -- so that neighborhoods can get to know the men and women who police them.

Will all this make a difference in Groveton?

There is skepticism and even some cynicism, especially in Gum Springs. One person who is not so sure is attorney William B. Moffitt, who wants citizen councils with real power. But even Moffit says: "Anything that is done in this community to improve relations between the people and the police has got to have some good in it. . . . It appears some positive things are being done."

Those words themselves are an indication that the police response has already made a not inconsiderable bit of difference.