#15488 ⟨a, b | aaa=ab, babbb=b⟩

Properties

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

# ab:aaa=ab,babbb=b b/a
bbbbbbbb=b
ba=bbbbb
aab=abbbbb
aaa=ab

Idempotents are shown in bold.

Idempotents are shown in bold.

Idempotents are shown in bold.

16 unique, 68 total

Σ	#	Presentation	Description	Related
10	4375	⟨a, b \| aaaa=b, abbbb=1⟩	Isomorphic to ℤ₁₇	39 iso
10	6428	⟨a, b \| aab=b, babbb=a⟩	Finite non-commutative monoid with 17 elements	2 iso
10	6514	⟨a, b \| aba=b, baaab=a⟩	Finite non-commutative monoid with 17 elements
10	7152	⟨a, b \| bb=aa, abab=aa⟩	Finite non-commutative monoid with 17 elements
10	7153	⟨a, b \| bb=aa, abab=ab⟩	Finite non-commutative monoid with 17 elements
10	7154	⟨a, b \| bb=aa, abab=ba⟩	Finite non-commutative monoid with 17 elements
11	13141	⟨a, b \| aab=aaa, bbb=ab⟩	Finite non-commutative monoid with 17 elements
11	13142	⟨a, b \| aab=aaa, bbb=ba⟩	Finite non-commutative monoid with 17 elements
11	13151	⟨a, b \| aba=aaa, baa=bb⟩	Finite non-commutative monoid with 17 elements
11	13156	⟨a, b \| aba=aaa, bbb=ab⟩	Finite non-commutative monoid with 17 elements
11	13218	⟨a, b \| abb=aba, bbb=aa⟩	Finite non-commutative monoid with 17 elements
11	14395	⟨a, b \| aaaa=b, abbbb=a⟩	Isomorphic to ℕ_{(17 = 1)}	2 iso
11	14396	⟨a, b \| aaaa=b, abbbb=b⟩	Isomorphic to ℕ_{(17 = 4)}	2 iso
11	14698	⟨a, b \| aabb=a, baaaa=b⟩	Finite non-commutative monoid with 17 elements	1 iso, 6 anti-iso
11	16143	⟨a, b \| aab=aa, bbbb=ba⟩	Finite non-commutative monoid with 17 elements
11	16521	⟨a, b \| aab=bb, bab=aaa⟩	Finite non-commutative monoid with 17 elements

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

3 total

Σ	#	Presentation	Mapping
11	15496	⟨a, b \| aaa=ab, bbabb=b⟩	φ(a) = a, φ(b) = b
11	15500	⟨a, b \| aaa=ab, bbbab=b⟩	φ(a) = a, φ(b) = b
11	15502	⟨a, b \| aaa=ab, bbbba=b⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#15491 ⟨a, b \| aaa=ab, bbaab=a⟩