〈a, b | bb=aa, abab=ba〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁷ ⇒ a³
ba⁵ ⇒ ba
a²b ⇒ ba²
b² ⇒ a²
bab ⇒ aba³

Idempotents

2 elements

1
a⁴

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
1	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
a	a	a²	ab	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²
b	b	ba	a²	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³
a²	a²	a³	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²
ab	ab	aba	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba
ba	ba	ba²	aba³	ba³	a⁴	aba⁴	ba⁴	a⁵	aba	ba	a⁶	aba²	ba²	a³	aba³	ba³	a⁴
a³	a³	a⁴	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴
aba	aba	aba²	ba	aba³	a⁵	ba²	aba⁴	a⁶	ba³	aba	a³	ba⁴	aba²	a⁴	ba	aba³	a⁵
ba²	ba²	ba³	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba
a⁴	a⁴	a⁵	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
aba²	aba²	aba³	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³
ba³	ba³	ba⁴	aba	ba	a⁶	aba²	ba²	a³	aba³	ba³	a⁴	aba⁴	ba⁴	a⁵	aba	ba	a⁶
a⁵	a⁵	a⁶	aba⁴	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²
aba³	aba³	aba⁴	ba³	aba	a³	ba⁴	aba²	a⁴	ba	aba³	a⁵	ba²	aba⁴	a⁶	ba³	aba	a³
ba⁴	ba⁴	ba	a⁶	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³
a⁶	a⁶	a³	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²
aba⁴	aba⁴	aba	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba

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
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 \| 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