〈a, b | abb=aba, bbb=aa〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right ab

Complete rewriting system

ab² ⇒ aba
ba² ⇒ a²b
b³ ⇒ a²
a³b ⇒ a⁴
(ab)² ⇒ a³
a⁵ ⇒ a⁴

Idempotents

2 elements

1
a⁴

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	b²	a³	a²b	aba	bab	b²a	a⁴	a²ba	(ba)²	b²ab	b(ba)²
1	1	a	b	a²	ab	ba	b²	a³	a²b	aba	bab	b²a	a⁴	a²ba	(ba)²	b²ab	b(ba)²
a	a	a²	ab	a³	a²b	aba	aba	a⁴	a⁴	a²ba	a³	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
b	b	ba	b²	a²b	bab	b²a	a²	a²ba	a²ba	(ba)²	b²ab	a³	a⁴	a⁴	b(ba)²	a⁴	a⁴
a²	a²	a³	a²b	a⁴	a⁴	a²ba	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
ab	ab	aba	aba	a⁴	a³	a⁴	a³	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
ba	ba	a²b	bab	a²ba	a²ba	(ba)²	(ba)²	a⁴	a⁴	a⁴	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
b²	b²	b²a	a²	a²ba	b²ab	a³	a²b	a⁴	a⁴	b(ba)²	a⁴	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴
a³	a³	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
a²b	a²b	a²ba	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
aba	aba	a⁴	a³	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
bab	bab	(ba)²	(ba)²	a⁴	a²ba	a⁴	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
b²a	b²a	a²ba	b²ab	a⁴	a⁴	b(ba)²	b(ba)²	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
a²ba	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
(ba)²	(ba)²	a⁴	a²ba	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
b²ab	b²ab	b(ba)²	b(ba)²	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴
b(ba)²	b(ba)²	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴	a⁴

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, baa=bb〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aba=aaa, bbb=ab〉	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