〈a, b | aba=aaa, baa=bb〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁷ ⇒ a⁶
ba⁵ ⇒ ba⁴
aba ⇒ a³
a⁴b ⇒ a⁶
b² ⇒ ba²
ba²b ⇒ ba⁴

Idempotents

3 elements

1
a⁶
ba⁴

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	a²b	ba²	bab	a⁴	a³b	ba³	a⁵	ba⁴	ba³b	a⁶
1	1	a	b	a²	ab	ba	a³	a²b	ba²	bab	a⁴	a³b	ba³	a⁵	ba⁴	ba³b	a⁶
a	a	a²	ab	a³	a²b	a³	a⁴	a³b	a⁴	a³b	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶
b	b	ba	ba²	ba²	bab	ba³	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a²	a²	a³	a²b	a⁴	a³b	a⁴	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ab	ab	a³	a⁴	a⁴	a³b	a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba	ba	ba²	bab	ba³	ba⁴	ba³	ba⁴	ba³b	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a³	a³	a⁴	a³b	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
a²b	a²b	a⁴	a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba²	ba²	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
bab	bab	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁴	a⁴	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
a³b	a³b	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba³	ba³	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
ba³b	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

19 unique, 71 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaaa=b, abbbb=1〉	Isomorphic to ℤ₁₇	39 isomorphic
10	〈a, b \| aab=b, babbb=a〉	Finite non-commutative monoid with 17 elements	1 isomorphic
10	〈a, b \| aba=b, baaab=a〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| aba=b, babbb=a〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=aa〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=ab〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=aaa, bbb=ab〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=aaa, bbb=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aba=aaa, bbb=ab〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| abb=aba, bbb=aa〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aaaa=b, abbbb=a〉	Finite commutative monoid with 17 elements	2 isomorphic
11	〈a, b \| aaaa=b, abbbb=b〉	Finite commutative monoid with 17 elements	2 isomorphic
11	〈a, b \| aabb=a, baaaa=b〉	Finite non-commutative monoid with 17 elements	1 isomorphic
11	〈a, b \| abba=a, aaaab=b〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aaa=ab, babbb=b〉	Finite non-commutative monoid with 17 elements	3 isomorphic
11	〈a, b \| aab=aa, bbbb=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=bb, bab=aaa〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=b, abbbba=a〉	Finite non-commutative monoid with 17 elements	4 isomorphic