How can I identify and generate a new variable that identifies which observations belong to different groups. Say I have the following dataset:

ID | country | side 
1 | arg | 1
1 | usa | 0
2 | ita | 1
2 | usa | 0
2 | uk | 1
3 | aus | 0
3 | uk | 1

and I want to create a new variable (sideUK) that identifies whether country "uk" was involved in ID and side of each country. So for example this would be:

ID | country | side | sideuk
1 | arg | 1 | 0
1 | usa | 0 | 0
2 | ita | 1 | 1
2 | usa | 0 | 0
2 | uk | 1 | 1
3 | aus | 0 | 0
3 | uk | 1 | 1

I'm not entirely sure what you're after, but the following reproduces your expected output

library(dplyr)
df %>%
 group_by(ID) %>%
 mutate(sideuk = +("uk" %in% country & side == 1)) %>%
 ungroup()
## A tibble: 7 x 4
# ID country side sideuk
# <int> <fct> <int> <int>
#1 1 arg 1 0
#2 1 usa 0 0
#3 2 ita 1 1
#4 2 usa 0 0
#5 2 uk 1 1
#6 3 aus 0 0
#7 3 uk 1 1

Sample data

df <- read.table(text =
 "ID country side
1 arg 1
1 usa 0
2 ita 1
2 usa 0
2 uk 1
3 aus 0
3 uk 1", header = T)

You want to group by ID and then check for 'uk' in the country variable

df %>%
 group_by(ID, side) %>%
 mutate(sideuk = as.integer('uk' %in% country))

# A tibble: 7 x 4
# Groups: ID, side [6]
 ID country side sideuk
 <dbl> <fct> <dbl> <int>
1 1 arg 1 0
2 1 usa 0 0
3 2 ita 1 1
4 2 usa 0 0
5 2 uk 1 1
6 3 aus 0 0
7 3 uk 1 1

I am not sure if this is what you are looking for. It is a solution without external libraries:

df$sideuk <- apply(df, 1, function(row) 
 return(
 as.integer(any(df[df$ID==row["ID"] & df$country=="uk" & row["side"] == 1, "side"]))
 )
)

Returns:

 ID country side sideuk
1 1 arg 1 0
2 1 usa 0 0
3 2 ita 1 1
4 2 usa 0 0
5 2 uk 1 1
6 3 aus 0 0
7 3 uk 1 1
8 4 mx 1 0
9 4 uk 0 0

Sample data

df <- read.table(text =
 "ID country side
 1 arg 1
 1 usa 0
 2 ita 1
 2 usa 0
 2 uk 1
 3 aus 0
 3 uk 1
 4 mx 1
 4 uk 0", header = T)