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a, b | aaa=a, ababba=b

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a3a
  2. a2bb
  3. ba2b
  4. bab2aba
  5. b3a(ab)3
  6. b(ba)2ab2ab
  7. (ba)3ab3
  8. b5b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2abbab2abaab2babb2ab3(ab)2ab2a(ba)2bab2b3ab4a(ba)2b(ab)2bab2ab4a(ba)3
11aba2abbab2abaab2babb2ab3(ab)2ab2a(ba)2bab2b3ab4a(ba)2b(ab)2bab2ab4a(ba)3
aaa2abababaab2bab2(ab)2ab2a(ba)3babb2aa(ba)2bab2ab(ab)2b4a(ba)2b3abab2b4b3
bbbab2bbabb2ab3(ba)2bab2abab3ab4b(ab)2bab2aab(ab)2b4ab(ba)3ab2a(ba)2baab2a
a2a2aba2abbab2abaab2babb2ab3(ab)2ab2a(ba)2bab2b3ab4a(ba)2b(ab)2bab2ab4a(ba)3
abababaab2ab(ab)2ab2a(ba)3a(ba)2bab2abab(ab)2b4ab3abab2bbabb4abb3b2(ba)2abab2a
bababbabbab2(ba)2bab2b2ab3b(ab)2bab2aab2aabab3a(ba)3a(ba)2ab2baabb4a(ab)2bb4
b2b2b2ab3b2abab3ab4ab(ab)2(ba)2b4abab2a(ba)2babb(ab)2bab2ab2abab2(ba)3b2abab2a
abaabaab(ab)2abaab2a(ba)2bab2aab2a(ba)3b3abab2b2abab(ab)2b3(ba)2b2ababb4bababb4a
ab2ab2ab2a(ba)3ab2bab(ab)2b4abbaba(ba)2b4abb2(ba)2(ab)2b3aabaab2b2abab2ab3ab2abab2
babbab(ba)2bab2babb(ab)2bab2aab2a(ba)3a(ba)2b2aab2bab4a(ab)2b2ababbabb4b3ab(ba)2b3a
b2ab2ab2abab2ab3ab(ab)2b3ab4ab2a(ba)2bab2a(ba)2b4aab2a(ba)3bab2b2ababbab(ab)2b2b
b3b3b3ab4b3(ba)2b4abbabb(ab)2abbab2bab2(ba)3abaab2b2ab3bab2a(ab)2ab2ab3aa(ba)2
(ab)2(ab)2a(ba)2bab2a(ab)2b3abab2b2ab3(ba)2ab2ab2abab4babab2baab(ab)2b4a(ba)3ba(ba)2b(ab)2
ab2aab2aab2baab2a(ba)3bbabb(ab)2b4ab2(ba)2bab2a(ba)2b4b2ab3bab2aab2a(ab)2abab3aab2ab
(ba)2(ba)2babb(ab)2(ba)2bab2(ba)3a(ba)2bab2aab2ab4a(ab)2b3ab2aab2b4abb3(ba)2b2babababba
bab2bab2bab2aab2abab2b2aab2bab2aba(ba)3bbabb3abb(ab)2b4a(ba)2bab2b3aa(ba)2b4bab2a(ab)2
b3ab3ab3(ba)2b3ab4babb(ab)2b4abbab2(ba)3a(ba)2abbabab2aab2a(ab)2b3aabab2aab2b3b2
b4b4b4abb4abbab2abaab2babb2ab3(ab)2ab2a(ba)2bab2b3ab4a(ba)2b(ab)2bab2ab4a(ba)3
a(ba)2a(ba)2(ab)2b3aa(ba)2bab2ab3(ba)2bab2b2ab4babb(ab)2ab2ab2b4ab(ba)3a(ba)2ab2abba(ab)2aba
b(ab)2b(ab)2(ba)3a(ba)2b(ab)2b4a(ab)2b3ab4abbab2ab3(ba)2bababab2b2ababb(ab)2baab2ab2(ba)3ab2
bab2abab2abab2b2abab2aab2ab2abaab2bab3ab(ab)2(ba)3bb3ab4a(ba)2bab2ab(ab)2(ba)2b4abab2bab
b4ab4ab4abb4ababaab2bab2(ab)2ab2a(ba)3babb2aa(ba)2bab2ab(ab)2b4a(ba)2b3abab2b4b3
(ba)3(ba)3b(ab)2b4a(ba)3a(ba)2b4ab(ab)2b3ababaab2bab2ab3bab2ab2a(ba)3bab2babb2ab(ab)2(ba)2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

1 unique, 1 total

Length:Presentation:Description:Related:
11 a, b | aba=b, baab=aaa Finite non-commutative monoid with 23 elements