SILVER GROVE - This city is so small that practically all of the children walk to school, there's no high school football team, and townspeople have to pick up their daily mail at the post office because there's no home delivery.

But that's just the way the town's 1,137 residents like it.

Typical of them is Mayor Carl John Schwarber, born in Silver Grove 56 years ago, who built his present home on East River Road one block from where his parents lived. All three of his children graduated from Silver Grove Independent Schools, Kentucky's second-smallest school district.

''It's a nice, quiet community most of the time,'' said Mr. Schwarber, who described his hometown as ''one mile long and four blocks wide.''

''When the kids grow up, they want to stay here most of the time,'' said City Clerk Katherine Wright. She said the only thing stopping many of them is that ''there aren't enough houses to go around.''

Mrs. Wright, who previously served as town mayor, moved to Silver Grove from her home on the Pendleton-Campbell county line 32 years ago, after she and her husband grew weary of putting their six sons on school buses for several hours each day.

''When we started looking, I insisted I wanted a small community, some place where my boys could walk to school,'' Mrs. Wright said. ''This year is the first year that I don't have a child or a grandchild in (the Silver Grove school system).''

For many, the Silver Grove Independent School District, which houses 300 pupils in kindergarten through grade 12 under one roof, is the hub of the community.

''I guess the parents have always felt that because it was a neighborhood or community school, that they had a little more input about what was going on,'' said Diana Heidelberg, principal of Silver Grove Elementary.

While Silver Grove's students in grades K-12 may share the same library and lunchroom, and typically boast graduating classes of fewer than 20 students, the school does well academically.

Results from the Kentucky Instructional Education Results System (KIRIS) released in October showed 9- and 10-year-olds at Silver Grove Elementary surpassed their fourth-grade improvement goal, netting the district cash rewards for improving test results.

''This is an example of how we're making strides in trying to provide a quality education for our students,'' Ms. Heidelberg said.

Earlier this month, the tiny school was the setting for a Christmas program, drawing 100 people to hear music performed BY Silver Grove's junior high and high school band.

Afterward, many of them trooped over to the nearBY Silver Grove Park for hot chocolate and the city clerk's homemade cookies.

Besides school activities, the town turns out for the annual Silver Fest on Memorial Day weekend. Started in 1983 to show off new swings the city had purchased with a federal grant, the daylong event now features a flea market, rides and a parade that wends through most of the town.

''It's a close community,'' said Marie Remley, who retired as Silver Grove's postmaster in June, after serving in that position 24 years. ''Everybody comes to the post office every day, so they just kind of gather there. The post office and the school are the gathering spots.''

Mrs. Wright said: ''When you go to the post office, you know who's in the hospital, who's been sick, and who you need to send a card to.''

The town drew its name from a summer resort at the mouth of Four Mile Creek that was named for a large grove of silver poplar trees. But the city owes its existence to the C&O Railroad, which laid out the town in 1912 to house its employees.

''BY building the town around the (train) yards, the railroad could have a crew assembled in 20 minutes to half an hour and be ready to run a train out within an hour,'' said longtime resident Gerald Losey.

For 36 years, the railroad ran the town, managing everything from electricity and water to sewage treatment.

But in 1948, as the higher-paying railroad jobs slowly disappeared, the railroad decided it didn't need the little town and dropped it, Mr. Losey said.

On Jan. 2, 1951 - Mr. Losey's 40th birthday - the former railroad employee was sworn in as Silver Grove's first mayor, after residents incorporated the town.

While the railroad yards have since closed, the high school sports teams still go BY the nickname Big Trains.