Try
# This is how you create your data.frame
group<-c("A","A","A","A","A","B","B","C","C","C")
replicate<-c(1,2,3,4,5,1,2,1,2,3)
x<-data.frame(group,replicate) # here you don't need c()
# Here's my solution
Max <- tapply(x$replicate, x$group,max)
data.frame(x, max.per.group=rep(Max, table(x$group)))
group replicate max.per.group
1 A 1 5
2 A 2 5
3 A 3 5
4 A 4 5
5 A 5 5
6 B 1 2
7 B 2 2
8 C 1 3
9 C 2 3
10 C 3 3