groupoid

1. A magma: a set with a total binary operation.

2. A set with a partial binary operation that is associative and has inverses and identities.

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Here are some other words you could make with the letters groupoid, you can also
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Top Words by points	Points	Word Game
groupoid	12	Scrabble

2 Letters	Scrabble® Points
gi	3
id	3
od	3
oi	2
op	4
or	2
pi	4
po	4
go	3
do	3
up	4

3 Letters	Scrabble® Points
pod	6
urp	5
urd	4
upo	5
udo	4
org	4
oud	4
our	3
rug	4
pig	6
piu	5
rod	4
poi	5
poo	5
roo	3
dig	5
pro	5
pud	6
pug	6
pur	5
rid	4
rig	4
rip	5
gip	6
god	5
dip	6
dog	5
dor	4
dug	5
dui	4
goo	4
gor	4
duo	4
dup	6
gid	5

4 Letters	Scrabble® Points
prog	7
drip	7
puri	6
dorp	7
prod	7
prig	7
pour	6
dour	5
poor	6
door	5
rood	5
roup	6
updo	7
roid	5
pood	7
guid	6
grip	7
grid	6
gorp	7
goop	7
good	6
odor	5
ordo	5
giro	5
gird	6
duro	5
drug	6
drop	7
pogo	7

5 Letters	Scrabble® Points
droop	8
odour	6
proud	8
poori	7
pirog	8
guiro	6
gourd	7
group	8

6 Letters	Scrabble® Points
upgird	10
uropod	9

8 Letters	Scrabble® Points
groupoid	12