library(dplyr)
A <- data.frame(name = c('A', 'A', 'B', 'C', 'C', 'A', 'C', 'B', 'A'),
                number = c(1:9))
> A

  name number
1    A      1
2    A      2
3    B      3
4    C      4
5    C      5
6    A      6
7    C      7
8    B      8
9    A      9

B <- A %>%
  group_by(name) %>%
  summarise(number = min(number))
> B

Source: local data frame [3 x 2]

    name number
  (fctr)  (int)
1      A      1
2      B      3
3      C      4