〈a, b | aaa=ab, babbb=b〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁸ ⇒ b
ba ⇒ b⁵
a²b ⇒ ab⁵
a³ ⇒ ab

Idempotents

3 elements

1
b⁷
ab³

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷
1	1	a	b	a²	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷
a	a	a²	ab	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴
b	b	b⁵	b²	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵
a²	a²	ab	ab⁵	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab
ab	ab	ab⁵	ab²	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵
b²	b²	b⁶	b³	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶
ab²	ab²	ab⁶	ab³	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶
b³	b³	b⁷	b⁴	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷
ab³	ab³	ab⁷	ab⁴	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷
b⁴	b⁴	b	b⁵	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b
ab⁴	ab⁴	ab	ab⁵	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab
b⁵	b⁵	b²	b⁶	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²
ab⁵	ab⁵	ab²	ab⁶	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²
b⁶	b⁶	b³	b⁷	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³
ab⁶	ab⁶	ab³	ab⁷	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³
b⁷	b⁷	b⁴	b	b	b⁵	b²	b⁶	b³	b⁷	b⁴	b	b⁵	b²	b⁶	b³	b⁷	b⁴
ab⁷	ab⁷	ab⁴	ab	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴	ab	ab⁵	ab²	ab⁶	ab³	ab⁷	ab⁴

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

19 unique, 68 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 \| 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 \| 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

Other isomorphic instances

3 total

Length:	Presentation:
11	〈a, b \| aaa=ab, bbabb=b〉
11	〈a, b \| aaa=ab, bbbab=b〉
11	〈a, b \| aaa=ab, bbbba=b〉