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〈a, b | aaa=ab, bbbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a9 ⇒ a
  2. ab ⇒ a3
  3. b4 ⇒ 1

Idempotents

5 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 35 total

Length:Presentation:Description:Related:
9 〈a, b | aaab=a, bbbb=1〉 Finite non-commutative monoid with 36 elements 3 isomorphic, 3 anti-isomorphic
9 〈a, b | aaa=1, ababbb=1〉 Finite non-Abelian group with 36 elements 17 isomorphic
10 〈a, b | aaa=ab, bbbb=b〉 Finite non-commutative monoid with 36 elements
10 〈a, b | bb=aa, ababab=1〉 Finite non-Abelian group with 36 elements
10 〈a, b | aaa=1, baabbb=a〉 Finite non-Abelian group with 36 elements 4 isomorphic
11 〈a, b | abb=aaa, bbbb=b〉 Finite non-commutative monoid with 36 elements
11 〈a, b | aaa=ab, bbbb=bb〉 Finite non-commutative monoid with 36 elements
11 〈a, b | aab=a, bbbbbb=b〉 Finite non-commutative monoid with 36 elements

Other isomorphic instances

1 total

Length:Presentation:
11〈a, b | aaab=abb, bbbb=1〉

Other anti-isomorphic instances

5 total

Length:Presentation:
11〈a, b | aaab=bab, bbbb=1〉
11〈a, b | aaaa=1, aaabbb=b〉
11〈a, b | aaaa=1, abaabb=b〉
11〈a, b | aaaa=1, ababab=b〉
11〈a, b | aaaa=1, abbaab=b〉