#2074 ⟨a, b | aab=b, babb=a⟩

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Properties

Element profile

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. ba ⇒ ab
  2. a3 ⇒ a
  3. a2b ⇒ b
  4. b3 ⇒ a2 
# ab:aab=b,babb=a ab
ba=ab
aaa=a
aab=b
bbb=aa

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aba2abb2ab2
11aba2abb2ab2
aaa2ababab2b2
bbabb2bab2a2a
a2a2aba2abb2ab2
ababbab2abb2aa2
b2b2ab2a2b2abab
ab2ab2b2aab2a2abb

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

22 unique, 1203 total

Σ#PresentationDescriptionRelated
7116⟨a, b | aaa=b, abb=1⟩Isomorphic to ℤ7763 iso
8577⟨a, b | aaa=b, abb=a⟩Isomorphic to ℕ(7 = 1)59 iso
8578⟨a, b | aaa=b, abb=b⟩Isomorphic to ℕ(7 = 3)44 iso
8913⟨a, b | aa=b, abbb=b⟩Isomorphic to ℕ(7 = 2)82 iso
8937⟨a, b | ab=a, baaa=b⟩Finite non-commutative monoid with 7 elements54 iso, 12 anti-iso
91593⟨a, b | aaa=ab, baa=b⟩Finite non-commutative monoid with 7 elements1 iso, 2 anti-iso
91601⟨a, b | aaa=bb, aab=b⟩Finite commutative monoid with 7 elements5 iso
91620⟨a, b | aab=aa, bbb=a⟩Isomorphic to ℕ(7 = 6)35 iso
91632⟨a, b | aab=ab, bbb=a⟩Isomorphic to ℕ(7 = 4)50 iso
92231⟨a, b | ab=aa, aaa=bb⟩Finite non-commutative monoid with 7 elements3 iso
92271⟨a, b | bb=aa, aaa=ab⟩Finite non-commutative monoid with 7 elements1 iso, 2 anti-iso
93197⟨a, b | ab=a, bbb=baa⟩Finite non-commutative monoid with 7 elements5 iso
104162⟨a, b | abb=aab, bbb=a⟩Isomorphic to ℕ(7 = 5)42 iso
106251⟨a, b | aaa=a, aabba=b⟩Finite non-commutative monoid with 7 elements1 iso
108987⟨a, b | ab=a, aaaaa=bb⟩Finite commutative monoid with 7 elements5 iso
109108⟨a, b | ab=a, bbbbb=aa⟩Finite commutative monoid with 7 elements2 iso
109110⟨a, b | ab=a, bbbbb=ba⟩Finite non-commutative monoid with 7 elements1 iso
109263⟨a, b | ab=a, aaaa=bbb⟩Finite commutative monoid with 7 elements4 iso
109375⟨a, b | ab=a, bbba=bbb⟩Finite non-commutative monoid with 7 elements3 iso
109376⟨a, b | ab=a, bbbb=aaa⟩Finite commutative monoid with 7 elements3 iso
109382⟨a, b | ab=a, bbbb=bba⟩Finite non-commutative monoid with 7 elements1 iso
1114843⟨a, b | abba=b, aabab=a⟩Finite non-commutative monoid with 7 elements1 iso

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

20 total

Σ#PresentationMapping
92078⟨a, b | aab=b, bbab=a⟩φ(a) = a, φ(b) = b
92116⟨a, b | aba=b, abbb=a⟩φ(a) = a, φ(b) = b
92120⟨a, b | aba=b, babb=a⟩φ(a) = a, φ(b) = b
1118982⟨a, b | aab=b, aababb=a⟩φ(a) = a, φ(b) = b
1118986⟨a, b | aab=b, aabbab=a⟩φ(a) = a, φ(b) = b
1119002⟨a, b | aab=b, ababab=a⟩φ(a) = a, φ(b) = b
1119030⟨a, b | aab=b, baaabb=a⟩φ(a) = a, φ(b) = b
1119034⟨a, b | aab=b, baabab=a⟩φ(a) = a, φ(b) = b
1119042⟨a, b | aab=b, babaab=a⟩φ(a) = a, φ(b) = b
1119058⟨a, b | aab=b, bbaaab=a⟩φ(a) = a, φ(b) = b
1119174⟨a, b | aba=b, aaabbb=a⟩φ(a) = a, φ(b) = b
1119180⟨a, b | aba=b, aababb=a⟩φ(a) = a, φ(b) = b
1119184⟨a, b | aba=b, aabbab=a⟩φ(a) = a, φ(b) = b
1119186⟨a, b | aba=b, aabbba=a⟩φ(a) = a, φ(b) = b
1119194⟨a, b | aba=b, abaabb=a⟩φ(a) = a, φ(b) = b
1119196⟨a, b | aba=b, ababab=a⟩φ(a) = a, φ(b) = b
1119198⟨a, b | aba=b, ababba=a⟩φ(a) = a, φ(b) = b
1119202⟨a, b | aba=b, abbaab=a⟩φ(a) = a, φ(b) = b
1119214⟨a, b | aba=b, baaabb=a⟩φ(a) = a, φ(b) = b
1119216⟨a, b | aba=b, baabab=a⟩φ(a) = a, φ(b) = b