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〈a, b | aba=bb, baaab=a〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 20 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁷ ⇒ a
aba⁶ ⇒ ab
a²b ⇒ ba²
b² ⇒ aba
bab ⇒ a⁵

Idempotents

2 elements

1
a⁶

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba⁵	aba⁵	ba⁶
1	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba⁵	aba⁵	ba⁶
a	a	a²	ab	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	a⁶	ba⁵	aba⁴	a	ba⁶	aba⁵	ba	ab
b	b	ba	aba	ba²	a⁵	aba²	ba³	a⁶	aba³	ba⁴	a	aba⁴	ba⁵	a²	aba⁵	ba⁶	a³	ab	a⁴	aba
a²	a²	a³	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba⁵	a	aba⁵	ba⁶	a²	ab	ba	aba	ba²
ab	ab	aba	ba³	aba²	a⁶	ba⁴	aba³	a	ba⁵	aba⁴	a²	ba⁶	aba⁵	a³	ba	ab	a⁴	ba²	a⁵	ba³
ba	ba	ba²	a⁵	ba³	aba³	a⁶	ba⁴	aba⁴	a	ba⁵	aba⁵	a²	ba⁶	ab	a³	ba	aba	a⁴	aba²	a⁵
a³	a³	a⁴	aba²	a⁵	ba⁴	aba³	a⁶	ba⁵	aba⁴	a	ba⁶	aba⁵	a²	ba	ab	a³	ba²	aba	ba³	aba²
aba	aba	aba²	a⁶	aba³	ba⁵	a	aba⁴	ba⁶	a²	aba⁵	ba	a³	ab	ba²	a⁴	aba	ba³	a⁵	ba⁴	a⁶
ba²	ba²	ba³	aba³	ba⁴	a	aba⁴	ba⁵	a²	aba⁵	ba⁶	a³	ab	ba	a⁴	aba	ba²	a⁵	aba²	a⁶	aba³
a⁴	a⁴	a⁵	ba⁴	a⁶	aba⁴	ba⁵	a	aba⁵	ba⁶	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	aba³	ba⁴
aba²	aba²	aba³	ba⁵	aba⁴	a²	ba⁶	aba⁵	a³	ba	ab	a⁴	ba²	aba	a⁵	ba³	aba²	a⁶	ba⁴	a	ba⁵
ba³	ba³	ba⁴	a	ba⁵	aba⁵	a²	ba⁶	ab	a³	ba	aba	a⁴	ba²	aba²	a⁵	ba³	aba³	a⁶	aba⁴	a
a⁵	a⁵	a⁶	aba⁴	a	ba⁶	aba⁵	a²	ba	ab	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	ba⁵	aba⁴
aba³	aba³	aba⁴	a²	aba⁵	ba	a³	ab	ba²	a⁴	aba	ba³	a⁵	aba²	ba⁴	a⁶	aba³	ba⁵	a	ba⁶	a²
ba⁴	ba⁴	ba⁵	aba⁵	ba⁶	a³	ab	ba	a⁴	aba	ba²	a⁵	aba²	ba³	a⁶	aba³	ba⁴	a	aba⁴	a²	aba⁵
a⁶	a⁶	a	ba⁶	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba⁵	aba⁵	ba⁶
aba⁴	aba⁴	aba⁵	ba	ab	a⁴	ba²	aba	a⁵	ba³	aba²	a⁶	ba⁴	aba³	a	ba⁵	aba⁴	a²	ba⁶	a³	ba
ba⁵	ba⁵	ba⁶	a³	ba	aba	a⁴	ba²	aba²	a⁵	ba³	aba³	a⁶	ba⁴	aba⁴	a	ba⁵	aba⁵	a²	ab	a³
aba⁵	aba⁵	ab	a⁴	aba	ba³	a⁵	aba²	ba⁴	a⁶	aba³	ba⁵	a	aba⁴	ba⁶	a²	aba⁵	ba	a³	ba²	a⁴
ba⁶	ba⁶	ba	aba	ba²	a⁵	aba²	ba³	a⁶	aba³	ba⁴	a	aba⁴	ba⁵	a²	aba⁵	ba⁶	a³	ab	a⁴	aba

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 65 total

Length:	Presentation:	Description:	Related:
8	〈a, b \| aab=a, bbbb=1〉	Finite non-commutative monoid with 20 elements	3 isomorphic, 1 anti-isomorphic
8	〈a, b \| ab=aa, bbbb=1〉	Finite non-commutative monoid with 20 elements	1 isomorphic
9	〈a, b \| abab=a, bbbb=1〉	Finite non-commutative monoid with 20 elements	2 isomorphic
9	〈a, b \| aba=ab, bbbb=1〉	Finite non-commutative monoid with 20 elements	1 isomorphic, 1 anti-isomorphic
9	〈a, b \| ab=aa, bbbb=b〉	Finite non-commutative monoid with 20 elements
10	〈a, b \| abb=aab, aaaa=1〉	Finite non-commutative monoid with 20 elements	2 isomorphic
10	〈a, b \| baa=abb, abab=1〉	Finite non-Abelian group with 20 elements	1 isomorphic, 1 anti-isomorphic
10	〈a, b \| aaaaa=1, abbbb=1〉	Isomorphic to ℤ₂₀	16 isomorphic
10	〈a, b \| aab=bb, aaaa=a〉	Finite non-commutative monoid with 20 elements
10	〈a, b \| aaa=bb, bab=aa〉	Finite non-commutative monoid with 20 elements	1 isomorphic
10	〈a, b \| aba=a, aaaa=bb〉	Finite non-commutative monoid with 20 elements
10	〈a, b \| aba=b, aaaa=bb〉	Finite non-commutative monoid with 20 elements
10	〈a, b \| ab=aa, bbbb=bb〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aaaa=aa, abbb=b〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aaab=bb, bbba=a〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aaaa=a, bbbbb=a〉	Finite commutative monoid with 20 elements
11	〈a, b \| aaaa=b, bbbbb=a〉	Finite commutative monoid with 20 elements
11	〈a, b \| aaaa=b, bbbbb=b〉	Finite commutative monoid with 20 elements
11	〈a, b \| aab=ba, abbabb=1〉	Finite non-Abelian group with 20 elements	2 isomorphic
11	〈a, b \| aab=aa, baba=bb〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aba=aa, aaaa=bb〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aba=aa, aaab=bb〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aba=bb, abb=aaa〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| aaaa=1, aaabab=b〉	Finite non-commutative monoid with 20 elements	1 isomorphic
11	〈a, b \| aaaa=1, aabab=ab〉	Finite non-commutative monoid with 20 elements	1 isomorphic
11	〈a, b \| aba=b, aaaaabb=1〉	Finite non-Abelian group with 20 elements	3 isomorphic
11	〈a, b \| aab=a, bbbbb=bb〉	Finite non-commutative monoid with 20 elements
11	〈a, b \| ab=aa, bbbb=bbb〉	Finite non-commutative monoid with 20 elements