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〈a, b | aaba=bb, aaaaa=1〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ 1
  2. b2 ⇒ a2ba
  3. ba4b ⇒ a4ba3
  4. (ab)2 ⇒ ba3ba4
  5. aba3b ⇒ (ba2)2
  6. a(a2b)2 ⇒ baba4
  7. b(a2b)2 ⇒ a3ba2

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

11 unique, 37 total

Length:Presentation:Description:Related:
9 〈a, b | aaba=b, bbbb=1〉 Finite non-Abelian group with 60 elements 4 isomorphic, 5 anti-isomorphic
10 〈a, b | aaba=bb, bbbb=1〉 Finite non-Abelian group with 60 elements 2 isomorphic
10 〈a, b | aaaa=1, aababb=1〉 Finite non-Abelian group with 60 elements 3 isomorphic
10 〈a, b | aaaa=1, baabb=a〉 Finite non-Abelian group with 60 elements
11 〈a, b | baabb=a, bbbbb=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | aabb=ba, aaaaa=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | baa=abb, aaaaa=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | aaba=b, abbabb=1〉 Finite non-Abelian group with 60 elements 2 isomorphic
11 〈a, b | aaaa=1, baabab=a〉 Finite non-Abelian group with 60 elements
11 〈a, b | aa=1, ababbabbb=1〉 Finite non-Abelian group with 60 elements 4 isomorphic
11 〈a, b | aa=1, ababbbabb=1〉 Finite non-Abelian group with 60 elements 6 isomorphic