#7153 ⟨a, b | bb=aa, abab=ab⟩

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:bb=aa,abab=ab b/a
bbbbbbbb=bbbb
abbbb=bbbbbbb
babbb=bbb
bba=abb
aa=bb
abab=ab

Idempotents are shown in bold.

	1	a	b	ab	ba	b²	aba	ab²	bab	b³	ab³	(ba)²	bab²	b⁴	b⁵	b⁶	b⁷
1	1	a	b	ab	ba	b²	aba	ab²	bab	b³	ab³	(ba)²	bab²	b⁴	b⁵	b⁶	b⁷
a	a	b²	ab	b³	aba	ab²	bab²	b⁴	ab	ab³	b⁵	aba	ab²	b⁷	b⁴	b⁵	b⁶
b	b	ba	b²	bab	ab²	b³	(ba)²	bab²	ab³	b⁴	b³	ab²	b⁷	b⁵	b⁶	b⁷	b⁴
ab	ab	aba	ab²	ab	b⁴	ab³	aba	ab²	b⁵	b⁷	ab³	b⁴	b⁶	b⁴	b⁵	b⁶	b⁷
ba	ba	b³	bab	b⁴	(ba)²	bab²	b⁷	b⁵	bab	b³	b⁶	(ba)²	bab²	b⁴	b⁵	b⁶	b⁷
b²	b²	ab²	b³	ab³	bab²	b⁴	ab²	b⁷	b³	b⁵	b⁴	bab²	b⁴	b⁶	b⁷	b⁴	b⁵
aba	aba	ab³	ab	b⁷	aba	ab²	b⁶	b⁴	ab	ab³	b⁵	aba	ab²	b⁷	b⁴	b⁵	b⁶
ab²	ab²	b⁴	ab³	b⁵	ab²	b⁷	b⁴	b⁶	ab³	b⁴	b⁷	ab²	b⁷	b⁵	b⁶	b⁷	b⁴
bab	bab	(ba)²	bab²	bab	b⁵	b³	(ba)²	bab²	b⁶	b⁴	b³	b⁵	b⁷	b⁵	b⁶	b⁷	b⁴
b³	b³	bab²	b⁴	b³	b⁷	b⁵	bab²	b⁴	b⁴	b⁶	b⁵	b⁷	b⁵	b⁷	b⁴	b⁵	b⁶
ab³	ab³	ab²	b⁷	ab³	b⁶	b⁴	ab²	b⁷	b⁷	b⁵	b⁴	b⁶	b⁴	b⁶	b⁷	b⁴	b⁵
(ba)²	(ba)²	b³	bab	b⁴	(ba)²	bab²	b⁷	b⁵	bab	b³	b⁶	(ba)²	bab²	b⁴	b⁵	b⁶	b⁷
bab²	bab²	b⁵	b³	b⁶	bab²	b⁴	b⁵	b⁷	b³	b⁵	b⁴	bab²	b⁴	b⁶	b⁷	b⁴	b⁵
b⁴	b⁴	b⁷	b⁵	b⁴	b⁴	b⁶	b⁷	b⁵	b⁵	b⁷	b⁶	b⁴	b⁶	b⁴	b⁵	b⁶	b⁷
b⁵	b⁵	b⁴	b⁶	b⁵	b⁵	b⁷	b⁴	b⁶	b⁶	b⁴	b⁷	b⁵	b⁷	b⁵	b⁶	b⁷	b⁴
b⁶	b⁶	b⁵	b⁷	b⁶	b⁶	b⁴	b⁵	b⁷	b⁷	b⁵	b⁴	b⁶	b⁴	b⁶	b⁷	b⁴	b⁵
b⁷	b⁷	b⁶	b⁴	b⁷	b⁷	b⁵	b⁶	b⁴	b⁴	b⁶	b⁵	b⁷	b⁵	b⁷	b⁴	b⁵	b⁶

Idempotents are shown in bold.

Idempotents are shown in bold.

16 unique, 71 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	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	15488	⟨a, b \| aaa=ab, babbb=b⟩	Finite non-commutative monoid with 17 elements	3 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

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