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〈a, b | aaa=1, abba=b〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. a3 ⇒ 1
  2. ba2 ⇒ ab2
  3. b2a ⇒ a2b
  4. bab2 ⇒ a2ba
  5. b5 ⇒ a(ba)2
  6. (ba)3 ⇒ (ab)3

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

14 unique, 86 total

Length:Presentation:Description:Related:
8 〈a, b | bab=aa, bbb=1〉 Finite non-commutative monoid with 27 elements 7 isomorphic
8 〈a, b | aaa=1, babb=a〉 Finite non-Abelian group with 27 elements 21 isomorphic
9 〈a, b | bab=aba, bbb=1〉 Finite non-commutative monoid with 27 elements 3 isomorphic
9 〈a, b | bab=aa, bbb=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
9 〈a, b | aaa=1, aabbab=1〉 Finite non-Abelian group with 27 elements 23 isomorphic
9 〈a, b | aaa=1, ababa=b〉 Finite non-commutative monoid with 27 elements 3 isomorphic
10 〈a, b | aaa=aa, aba=bb〉 Finite non-commutative monoid with 27 elements
10 〈a, b | aaa=1, abaaba=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
10 〈a, b | aaa=1, baab=aba〉 Finite non-commutative monoid with 27 elements 1 isomorphic
11 〈a, b | aaba=b, aaabbb=1〉 Finite non-Abelian group with 27 elements 7 isomorphic
11 〈a, b | aaba=b, aabbab=1〉 Finite non-Abelian group with 27 elements 5 isomorphic
11 〈a, b | aaa=bb, aabaa=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aaa=a, abbbbb=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aba=b, bbbb=aaa〉 Finite non-commutative monoid with 27 elements

Other isomorphic instances

7 total

Length:Presentation:
9〈a, b | baa=abb, bbb=1〉
10〈a, b | aaa=1, aabaa=bb〉
10〈a, b | aaa=1, aabba=ab〉
11〈a, b | aaa=1, aaaabba=b〉
11〈a, b | aaa=1, abaaaba=b〉
11〈a, b | aaa=1, abaa=aabb〉
11〈a, b | aaa=1, abba=aaab〉