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〈a, b | aa=a, ababab=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a2 ⇒ a
  2. ab2 ⇒ b2
  3. b2ab ⇒ b3
  4. b4 ⇒ b3
  5. (ab)3 ⇒ b2

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1ababbab2abababb2ab3(ab)2(ba)2b3aa(ba)2b(ab)2(ba)3
11ababbab2abababb2ab3(ab)2(ba)2b3aa(ba)2b(ab)2(ba)3
aaaabababab2aba(ab)2b2ab3(ab)2a(ba)2b3aa(ba)2b2b2a
bbbab2babb2ab3(ba)2b3b3ab3b(ab)2b3ab3a(ba)3b3b3a
abababab2(ab)2b2ab3a(ba)2b3b3ab3b2b3ab3ab2ab3b3a
bababababbab(ba)2b3(ba)2b(ab)2b3ab3b(ab)2(ba)3b3a(ba)3b3b3a
b2b2b2ab3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a
abaabaaba(ab)2(ab)2a(ba)2b3a(ba)2b2b3ab3b2b2ab3ab2ab3b3a
babbab(ba)2b3b(ab)2b3ab3(ba)3b3b3ab3b3b3ab3ab3ab3b3a
b2ab2ab2ab3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a
b3b3b3ab3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a
(ab)2(ab)2a(ba)2b3b2b3ab3b2ab3b3ab3b3b3ab3ab3ab3b3a
(ba)2(ba)2(ba)2b(ab)2b(ab)2(ba)3b3(ba)3b3b3ab3b3b3ab3ab3ab3b3a
b3ab3ab3ab3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a
a(ba)2a(ba)2a(ba)2b2b2b2ab3b2ab3b3ab3b3b3ab3ab3ab3b3a
b(ab)2b(ab)2(ba)3b3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a
(ba)3(ba)3(ba)3b3b3b3ab3b3ab3b3ab3b3b3ab3ab3ab3b3a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 175 total

Length:Presentation:Description:Related:
8 〈a, b | bb=aa, abab=1〉 Finite non-Abelian group with 16 elements 4 isomorphic
8 〈a, b | aa=1, ababbb=1〉 Finite non-Abelian group with 16 elements 40 isomorphic
9 〈a, b | aaaa=b, bbbb=1〉 Isomorphic to ℤ16 67 isomorphic
9 〈a, b | aab=a, bbbb=b〉 Finite non-commutative monoid with 16 elements
10 〈a, b | aaab=ba, abab=1〉 Finite non-Abelian group with 16 elements 7 isomorphic
10 〈a, b | bab=aaa, aabb=1〉 Finite non-Abelian group with 16 elements 6 isomorphic
10 〈a, b | aaaa=a, aabb=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=a, bbbb=a〉 Finite commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=b, bbbb=a〉 Finite commutative monoid with 16 elements 5 isomorphic
10 〈a, b | aba=b, aaaabb=1〉 Finite non-Abelian group with 16 elements 3 isomorphic
10 〈a, b | aba=b, aabbbb=1〉 Finite non-Abelian group with 16 elements 5 isomorphic
11 〈a, b | aaaa=aa, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaaa=ab, bbbb=a〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aaaa=bb, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaab=bb, abba=a〉 Finite non-commutative monoid with 16 elements 2 isomorphic
11 〈a, b | bab=aab, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | bab=aba, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaaa=a, aabab=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
11 〈a, b | aab=bb, abbba=a〉 Finite non-commutative monoid with 16 elements 3 isomorphic
11 〈a, b | aaa=ab, babb=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=ab, bbaa=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=bb, abab=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aba=aa, bbbb=ab〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=b, abbbbb=b〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aba=b, aaaa=abb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | ab=aa, bbba=bbb〉 Finite non-commutative monoid with 16 elements