Folks in this isolated mill city of 80,000 on the banks of the Chattahoochee River, which separates Georgia from Alabama, have wanted the rest of America to hear the name Columbus.

They wanted America to know Columbus had a historic district and one of the most beautiful theatres in the South, gorgeous tree-lined neighborhoods, friendly people and relaxed, peaceful Southern atmosphere.

The city fathers didn't want to change Columbus much, but they wanted the rest of the country to know where it is. A new Chamber of Commerce president was hired to promote Columbus, the city was finally to be added to the interstate system and the Columbus promoters were quick to point out the town finds itself only 50 miles from what used to be the even more obscure town of Plains.

But in 1977 the dream of promoting Columbus as a lovely, small, quaint Southern city was swept away by a reality of random violence. It was a new reality for Columbus and one which citizens here fought hard not to accept.

If the rest of America was to hear of Columbus tale of the New South, it was to hear of it because one of the most savage series of crime in the history of the South happened here - the rape-strangling of five elderly Columbus women in their homes.

Like other small cities, Columbus had always had the kind of sin and intrigue people were used to - men being shot by husbands of the other women and drunken gunfights. What people here see as being new is the impersonal violence between killer and victim who have never met, observers say.

Mary Margaret Byrne, an editor and lifelong resident and observer of Columbus, said, "Violent death always shocks you. "But in the south, most people who kill each other know each other. The terrible dehumanizing aspect to these crimes is that people here don't expect it. They think of that as a big-city crime. A typical Southern killing has whiskey, bad blood, and maybe law enforcement officers.

"Another thing about this that has so shocked and horrified people is that Southerners have a great deal of residual respect and devotion to elderly women, and this is true for blacks and whites alike - we're all influenced by our grandmothers - that's why this carries a special feeling of horror. Who would break in and kill and elderly lady and molest her so horribly? You've got to be bent to do this sort of thing, and it's always the kind of crime we thought only happened in New York and places like that."

Shock and outrage is almost palpable in the town, but more significant to some, the public errosion of confidence in the town's institutions.

The police have shown a genius for making the wrong moves. The mayor has been single-mindedly stubborn in his refusal to call on the Georgia Bureau of Investigation for help.

The force is led by Curtis McClung, the antithesis of the Southern sheriff stereotype. McClung is an articulate, hard-working chief of police who expects to receive his doctorate degree in a rehabilitation-related field this year. Nevertheless, McClung heads a department of men who are accustomed to drunken saloon shootouts, not mindless, apparently motiveless slayings.

While the police still grope to solve what the perceive as a new kind of crime McClung answers a question about the citizens' slow changes in perception.

"I know what you mean, kind of, 'Have we lost our innocence?' . . . Well, people feel we have an aberrant person in our midst and they are quite frustrated in our inability to 'apprehend.'"

The crimes have increased the awareness of his officers, too. When the first elderly strangling victim was found in September, 16 police began a routine investigation of the savage crime.

But when nine days later another woman, who lived alone in the same tree-lined attractive part of town, was killed with a nylon stocking and molested by an intruder in a crime the coroner called a "replay" of the first, there was a realization that the police faced a new kind of crime. And they used mostly old techniques.

A stakeout involving 45 or so officers staying in houses at night was tried, but was called off after 10 days when police jailed a 25-year-old illiterate, retarded man named Jerome Livas.

Livas was picked up originally in connection with the beating of his ex-girlfriend - who later died - but because the ex-girlfriend was 30 years older than Livas, police questioned him about the slayings.

But on Oct. 25, while Livas was in jail, the third woman was strangled and raped in her home - this one an 89-year-old partially crippled, nearly blind and deaf widow who was slain at midday.

Police stubbornly refused to discount Livas as a suspect, even though officers admitted that the only information against him was a "confession."

Four days after the third slaying with Livas still in jail - another elderly woman was raped and strangled in her home by a killer who silently dismantled her deadbolt lock.

But only after a sensational newspaper jailhouse interview with Livas, during which the dimwitted suspect signed a "confession" that he killed Presidents Kennedy and William McKinley, was with the Charles Manson family when they killed Sharon Tate and was in on the kidnaping of Charles Lindbergh's baby in the early 1930s, did the police admit they didn't have their man.

So in late October McClung ordered special patrols to cruise the neighborhoods where the stranglings had occurred, watching for suspicious signs.After seven weeks of fruitless searching, and as Columbusites began to dwell on Christmas, not their nagging fear, the patrols were stopped.

On a day some Columbus religious people call the fourth day of Christmas, a strangler struck again. This time the victim was Kathleen Woodruff, a wealthy member of the Woodruff clan associated with the Atlanta-based Coca-Cola conglormerate.

This week police had to admit that Woodruff's house was on the route where the special patrols had cruised before they were called off two weeks ago.

So it is that when a New York woman came to Columbus last month to direct a play at the theater the Chamber of Commerce is so proud of, she wasn't exposed to the question only a year ago routinely posed to residents who moved to Columbus from large Northern cities: "Aren't you afraid of the crime up there?"

Instead, for the month or so she was in Columbus the woman, who lives alone near Central Park, would not live alone here, and was afraid to spend time without the company of others.