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〈a, b | aba=b, baaaab=a〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 21 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a¹¹ ⇒ a
ba¹⁰ ⇒ b
ab ⇒ ba⁹
b² ⇒ a⁵

Idempotents

2 elements

1
a¹⁰

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹
1	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹
a	a	a²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a	ba⁸
b	b	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a	ba⁸	a²	ba⁹	a³	b	a⁴
a²	a²	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a	ba⁶	a²	ba⁷
ba	ba	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a	b	a²	ba	a³
a³	a³	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a	ba⁴	a²	ba⁵	a³	ba⁶
ba²	ba²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a	ba²	a²
a⁴	a⁴	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a	ba²	a²	ba³	a³	ba⁴	a⁴	ba⁵
ba³	ba³	ba⁴	a²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a
a⁵	a⁵	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴
ba⁴	ba⁴	ba⁵	a	ba⁶	a²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰
a⁶	a⁶	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a	ba⁸	a²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³
ba⁵	ba⁵	ba⁶	a¹⁰	ba⁷	a	ba⁸	a²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹
a⁷	a⁷	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a	ba⁶	a²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²
ba⁶	ba⁶	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸
a⁸	a⁸	a⁹	ba²	a¹⁰	ba³	a	ba⁴	a²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba
ba⁷	ba⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a	ba²	a²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷
a⁹	a⁹	a¹⁰	ba	a	ba²	a²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b
ba⁸	ba⁸	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a	ba⁴	a²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶
a¹⁰	a¹⁰	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹
ba⁹	ba⁹	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a	ba⁶	a²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

12 unique, 64 total

Length:	Presentation:	Description:	Related:
8	〈a, b \| aaa=ab, bbb=1〉	Finite non-commutative monoid with 21 elements	6 isomorphic, 9 anti-isomorphic
8	〈a, b \| aaa=1, abbb=b〉	Finite non-commutative monoid with 21 elements	10 isomorphic, 5 anti-isomorphic
9	〈a, b \| aaa=ab, bbb=b〉	Finite non-commutative monoid with 21 elements	1 anti-isomorphic
9	〈a, b \| aaa=1, babb=ab〉	Finite non-commutative monoid with 21 elements	6 isomorphic
10	〈a, b \| aaa=aa, bbb=ab〉	Finite non-commutative monoid with 21 elements
10	〈a, b \| aaa=a, abbbb=b〉	Finite non-commutative monoid with 21 elements
11	〈a, b \| aaaaa=b, abbbb=1〉	Isomorphic to ℤ₂₁	13 isomorphic
11	〈a, b \| bab=aaa, abba=b〉	Finite non-commutative monoid with 21 elements
11	〈a, b \| bab=aaa, bbb=aa〉	Finite non-commutative monoid with 21 elements
11	〈a, b \| aab=ba, ababab=1〉	Finite non-Abelian group with 21 elements	1 isomorphic
11	〈a, b \| aaa=a, ababbb=b〉	Finite non-commutative monoid with 21 elements	1 isomorphic
11	〈a, b \| aaa=1, abbab=aba〉	Finite non-commutative monoid with 21 elements