Perverted. Degenerate. Depraved. That's the consensus on the Alice Cooper band. On stage Cooper -- with his six-inch spiked heels, white tights, grotesque mascara, a boa constrictor draped around his neck -- simulates rape, necrophilia, plenty of S-M, cannibalism. His teenage audiences go wild over songs entitled ""Dead Babies"" and ""Raped and Freezing."" Cooper, the ultimate freak, dressed as a transvestite, is carefully groomed to be repulsive. As a social phenomenon he tends to inspire reflections on the sickness of our society. Greene, a journalist for the Chicago Sun-Times and the author of two prior books, spent some weeks traveling with the musicians. It was the holiday season and each night Greene, dressed as Santa Claus, was stomped to death by the band. The book that resulted is a notch better than most rock 'n' roll reportage. The Alice Cooper image, it turns out, is purest hype. The musicians are pros; their managers worry about mundane matters like scheduling, hotel reservations, busted spotlights, ticket sales. Alice himself is sometimes frightened of the nightmarish fantasy world he unleashes. He lives in quiet, faithful domesticity with his girlfriend of five years (""She doesn't like our music that much""); doesn't use drags and is squeamish at the thought of killing a cockroach. He describes himself as ""a romantic."" Greene plays up the incongruities between Alice on stage and off, but the Cooper spectacle cries out for social analysis. How can this fanged horror be the sex symbol of the young? Here, unfortunately, Greene draws a blank; the question is glaring, the answers elusive. In the end this is an entertaining glimpse of the dementia of rock stars at work and for many that will be enough. Greene is unprepared (as is Alice Cooper) to tell us what it all means.