Did Tigerclaw really kill Redtail

yes in Into the Wild

Yeah. In the first book of the warrior series Rusty (Firepaw's pet name, he hasn't gotten his clan name yet) enters the camp of thunderclan. A warrior runs into the camp in distress telling the clan about a battle that was happening at the time. Later on, they find that Redtail (The thunderclan deputy) was killed by an "Enemy from an other clan" but it was really tigerclaw in hopes that if he killed redtail that bluestar (The Thunderclan leader) would pick him as the next deputy.