#7152 ⟨a, b | bb=aa, abab=aa⟩

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=aa a/b
aaaaaaa=aaa
baaaaaa=baa
abaa=baaaaa
aab=baa
bb=aa
abab=aa

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	aba	ba²	bab	a⁴	ba³	(ba)²	a⁵	ba⁴	a⁶	ba⁵
1	1	a	b	a²	ab	ba	a³	aba	ba²	bab	a⁴	ba³	(ba)²	a⁵	ba⁴	a⁶	ba⁵
a	a	a²	ab	a³	ba²	aba	a⁴	ba³	ba⁵	a²	a⁵	ba²	a³	a⁶	ba³	a³	ba⁴
b	b	ba	a²	ba²	bab	a³	ba³	(ba)²	a⁴	ba⁵	ba⁴	a⁵	ba²	ba⁵	a⁶	ba²	a³
a²	a²	a³	ba²	a⁴	ba⁵	ba³	a⁵	ba²	ba⁴	a³	a⁶	ba⁵	a⁴	a³	ba²	a⁴	ba³
ab	ab	aba	a³	ba⁵	a²	a⁴	ba²	a³	a⁵	ba⁴	ba³	a⁶	ba⁵	ba⁴	a³	ba⁵	a⁴
ba	ba	ba²	bab	ba³	a⁴	(ba)²	ba⁴	a⁵	a³	ba²	ba⁵	a⁴	ba³	ba²	a⁵	ba³	a⁶
a³	a³	a⁴	ba⁵	a⁵	ba⁴	ba²	a⁶	ba⁵	ba³	a⁴	a³	ba⁴	a⁵	a⁴	ba⁵	a⁵	ba²
aba	aba	ba⁵	a²	ba²	a⁵	a³	ba³	a⁶	a⁴	ba⁵	ba⁴	a⁵	ba²	ba⁵	a⁶	ba²	a³
ba²	ba²	ba³	a⁴	ba⁴	a³	a⁵	ba⁵	a⁴	a⁶	ba³	ba²	a³	ba⁴	ba³	a⁴	ba⁴	a⁵
bab	bab	(ba)²	ba³	a³	ba²	ba⁴	a⁴	ba³	ba⁵	a⁶	a⁵	ba²	a³	a⁶	ba³	a³	ba⁴
a⁴	a⁴	a⁵	ba⁴	a⁶	ba³	ba⁵	a³	ba⁴	ba²	a⁵	a⁴	ba³	a⁶	a⁵	ba⁴	a⁶	ba⁵
ba³	ba³	ba⁴	a³	ba⁵	a⁶	a⁴	ba²	a³	a⁵	ba⁴	ba³	a⁶	ba⁵	ba⁴	a³	ba⁵	a⁴
(ba)²	(ba)²	a³	ba²	a⁴	ba⁵	ba³	a⁵	ba²	ba⁴	a³	a⁶	ba⁵	a⁴	a³	ba²	a⁴	ba³
a⁵	a⁵	a⁶	ba³	a³	ba²	ba⁴	a⁴	ba³	ba⁵	a⁶	a⁵	ba²	a³	a⁶	ba³	a³	ba⁴
ba⁴	ba⁴	ba⁵	a⁶	ba²	a⁵	a³	ba³	a⁶	a⁴	ba⁵	ba⁴	a⁵	ba²	ba⁵	a⁶	ba²	a³
a⁶	a⁶	a³	ba²	a⁴	ba⁵	ba³	a⁵	ba²	ba⁴	a³	a⁶	ba⁵	a⁴	a³	ba²	a⁴	ba³
ba⁵	ba⁵	ba²	a⁵	ba³	a⁴	a⁶	ba⁴	a⁵	a³	ba²	ba⁵	a⁴	ba³	ba²	a⁵	ba³	a⁶

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	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	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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