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〈a, b | aab=b, bbaa=aaa〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 15 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁵ ⇒ b
ab ⇒ b³
a³ ⇒ b²a²

Idempotents

4 elements

1
b⁴
b²a
b⁴a²

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²
1	1	a	b	a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²
a	a	a²	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b²a²
b	b	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	ba²
a²	a²	b²a²	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²
ba	ba	ba²	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b³a²
b²	b²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b²a²
ba²	ba²	b³a²	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	ba²
b²a	b²a	b²a²	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²
b³	b³	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b³a²
b²a²	b²a²	b⁴a²	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b²a²
b³a	b³a	b³a²	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	ba²
b⁴	b⁴	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²
b³a²	b³a²	ba²	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b³a²
b⁴a	b⁴a	b⁴a²	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b	b⁴a²	ba	b²	ba²	b²a	b²a²
b⁴a²	b⁴a²	b²a²	b	b⁴a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁴a²

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

23 unique, 190 total

Length:	Presentation:	Description:	Related:
9	〈a, b \| aaa=bb, aba=a〉	Finite non-commutative monoid with 15 elements	2 isomorphic
9	〈a, b \| aaa=bb, aba=b〉	Finite non-commutative monoid with 15 elements	1 isomorphic
9	〈a, b \| aaab=1, bbbbb=1〉	Isomorphic to ℤ₁₅	138 isomorphic
9	〈a, b \| aaa=a, abbb=b〉	Finite non-commutative monoid with 15 elements	4 isomorphic
10	〈a, b \| aaa=bb, aba=aa〉	Finite non-commutative monoid with 15 elements	1 isomorphic
10	〈a, b \| aaa=bb, aba=bb〉	Finite non-commutative monoid with 15 elements	2 isomorphic
10	〈a, b \| aaa=a, bbbbb=a〉	Finite commutative monoid with 15 elements
10	〈a, b \| aaa=b, bbbbb=a〉	Finite commutative monoid with 15 elements
10	〈a, b \| aaa=b, bbbbb=b〉	Finite commutative monoid with 15 elements
11	〈a, b \| abb=aaa, baaa=b〉	Finite non-commutative monoid with 15 elements	3 isomorphic
11	〈a, b \| abb=aaa, baba=b〉	Finite non-commutative monoid with 15 elements	1 isomorphic
11	〈a, b \| aab=aaa, aba=bb〉	Finite non-commutative monoid with 15 elements
11	〈a, b \| abb=aaa, bbb=ab〉	Finite non-commutative monoid with 15 elements	1 isomorphic
11	〈a, b \| abb=aaa, bbb=ba〉	Finite non-commutative monoid with 15 elements
11	〈a, b \| aaa=aa, bbbbb=a〉	Finite commutative monoid with 15 elements
11	〈a, b \| aaa=ab, baabb=b〉	Finite non-commutative monoid with 15 elements	5 isomorphic
11	〈a, b \| aaa=ab, bbbbb=a〉	Finite commutative monoid with 15 elements	1 isomorphic
11	〈a, b \| aaa=bb, bbbbb=a〉	Finite commutative monoid with 15 elements	1 isomorphic
11	〈a, b \| aaa=ab, bbbb=aa〉	Finite non-commutative monoid with 15 elements
11	〈a, b \| aab=aa, bbbb=ab〉	Finite non-commutative monoid with 15 elements
11	〈a, b \| aaa=b, bbbbb=ab〉	Finite commutative monoid with 15 elements
11	〈a, b \| aab=a, bbbbb=ba〉	Finite non-commutative monoid with 15 elements	1 anti-isomorphic
11	〈a, b \| ab=aa, bbaaa=bb〉	Finite non-commutative monoid with 15 elements	6 isomorphic