#1281 ⟨a, b | aaaaaaabba=1⟩

Properties

Sum of relation sides is 10
Infinite non-Abelian group
Element a⁶ba has infinite order
Inverses of generators:
- a^-1 = a⁷d
- b^-1 = bc
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaaaabb⟩
- Isomorphism: φ(a) = a, φ(b) = b

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

# ab:aaaaaaabba=1 abcd aaaaaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaaaaa=c

8 unique, 8 total

Σ	#	Presentation	Properties
10	1818	⟨a, b \| abbbbbbba=b⟩	Can Inf
10	1821	⟨a, b \| aaaaaaaa=bb⟩	Can Inf
10	2090	⟨a, b \| abbbbbba=bb⟩	Can Inf
10	2095	⟨a, b \| aaaaaaa=bab⟩	Can Inf
10	2362	⟨a, b \| abbbbba=bbb⟩	Can Inf
10	2370	⟨a, b \| aaaaaa=baab⟩	Can Inf
10	2634	⟨a, b \| abbbba=bbbb⟩	Can Inf
10	2741	⟨a, b \| baaab=aaaaa⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
10	1287	⟨a, b \| aaaaaabbaa=1⟩	φ(a) = a, φ(b) = b
10	1299	⟨a, b \| aaaaabbaaa=1⟩	φ(a) = a, φ(b) = b
10	1322	⟨a, b \| aaaabbaaaa=1⟩	φ(a) = a, φ(b) = b
10	1546	⟨a, b \| abbbbbbbba=1⟩	φ(a) = b, φ(b) = a