A citywide search for the beauty salon robbers who shot and killed a Fairfax County elementary school teacher while she was getting a shampoo ended Thursday night with the arrest of three Alexandria teen-agers.

The 15- and 16-year-old youths were charged yesterday with killing Muriel F. Hodan a 38-year-old former missionary while she sat in a swivel chair in the Parkway Beauty Salon on South Washington Street in Alexandria.

The shooting took place in the late afternoon on St. Patrick's Day after three youths parked bicycles outside the beauty salon and came inside asking for money.

The owner of the salon recalled yesterday that she gave the robbers her wallet, which had no money, and about $50 from the cash register. Then, the owner said, one robber with a small automatic pistol in his hand asked Muriel Hodan for her purse.

The teacher from Groveton Elementary School, who had patronized the salon every Friday for the past five years, stood and pointed to her white purse, the owner said. "Then he told her to sit down and then he shot her," she said.

The youths rushed outside, fired four shots into the sidewalk, dropped the pistol and fled north toward the center of Alexandria on their bicycles, the owner said.

An anonymous telephone call led Alexandria police to the three teenagers, according to Alexandria Commonwealth's Attorney William L. Cowhig.

The arrest came after almost a week of investigation by city police and detectives. The inquiry included several brush-beating searches for clues in the area around the beauty salon, the hypnotism of a witness to the shooting to obtain better descriptions of the robbers and the release of a composite drawing of the robber who allegedly shot Hodan.

The teen-agers, one 15 years old and the other two 16, will appear before the Alexandria Juvenile Court April 7. Cowhig said he will ask that their cases be transferred to Circuit Court so they can be tried as adults because of the seriousness of the crime.

Alexandria police said yesterday the composite drawing of one of the suspects led to a number of phone calls from areas residents who volunteered information.

The witness hypnotized Thursday by police was Hodan's 15-year-old nephew. The youth, who had been living with his aunt and past three months, accompanied her to the salon on the day of the murder. Police said the youth was put under hypnosis in an attempt to obtain a more detailed description of the robbers.

Hodan, a resident of Burke, spent five years as a missionary in Africa. She returned to the United States about five years ago, and received a master's degree in reading from George Washington University. She taught reading at Groveton Elementary.

The beauty salon where the murder took place is in the Hunting Towers shopping center, a small complex of seven businesses surrounded by brick apartment buildings. Armed robberies are not common in the area, shop proprietors said yesterday.

The High's Dairy store was robbed in January and the Chicken House has been robbed several times in past years, employes said yesterday.