#7154 ⟨a, b | bb=aa, abab=ba⟩

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=ba a/b
aaaaaaa=aaa
baaaaa=ba
aab=baa
bb=aa
bab=abaaa

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
1	1	a	b	a²	ab	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
a	a	a²	ab	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²
b	b	ba	a²	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³
a²	a²	a³	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²
ab	ab	aba	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba
ba	ba	ba²	aba³	ba³	a⁴	aba⁴	ba⁴	a⁵	aba	ba	a⁶	aba²	ba²	a³	aba³	ba³	a⁴
a³	a³	a⁴	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴
aba	aba	aba²	ba	aba³	a⁵	ba²	aba⁴	a⁶	ba³	aba	a³	ba⁴	aba²	a⁴	ba	aba³	a⁵
ba²	ba²	ba³	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba
a⁴	a⁴	a⁵	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴
aba²	aba²	aba³	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³
ba³	ba³	ba⁴	aba	ba	a⁶	aba²	ba²	a³	aba³	ba³	a⁴	aba⁴	ba⁴	a⁵	aba	ba	a⁶
a⁵	a⁵	a⁶	aba⁴	a³	ba²	aba	a⁴	ba³	aba²	a⁵	ba⁴	aba³	a⁶	ba	aba⁴	a³	ba²
aba³	aba³	aba⁴	ba³	aba	a³	ba⁴	aba²	a⁴	ba	aba³	a⁵	ba²	aba⁴	a⁶	ba³	aba	a³
ba⁴	ba⁴	ba	a⁶	ba²	aba³	a³	ba³	aba⁴	a⁴	ba⁴	aba	a⁵	ba	aba²	a⁶	ba²	aba³
a⁶	a⁶	a³	ba²	a⁴	aba²	ba³	a⁵	aba³	ba⁴	a⁶	aba⁴	ba	a³	aba	ba²	a⁴	aba²
aba⁴	aba⁴	aba	a³	aba²	ba	a⁴	aba³	ba²	a⁵	aba⁴	ba³	a⁶	aba	ba⁴	a³	aba²	ba

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	7153	⟨a, b \| bb=aa, abab=ab⟩	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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