#2783 ⟨a, b | aaaaaaaabba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element a⁷ba has infinite order
Inverses of generators:
- a^-1 = a⁸d
- b^-1 = bc
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaaaaabb⟩
- 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:aaaaaaaabba=1 abcd aaaaaaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaaaaaa=c

9 unique, 9 total

Σ	#	Presentation	Properties
11	3832	⟨a, b \| abbbbbbbba=b⟩	Can Inf
11	3835	⟨a, b \| aaaaaaaaa=bb⟩	Can Inf
11	4360	⟨a, b \| abbbbbbba=bb⟩	Can Inf
11	4365	⟨a, b \| aaaaaaaa=bab⟩	Can Inf
11	4888	⟨a, b \| abbbbbba=bbb⟩	Can Inf
11	4896	⟨a, b \| aaaaaaa=baab⟩	Can Inf
11	5416	⟨a, b \| abbbbba=bbbb⟩	Can Inf
11	5431	⟨a, b \| aaaaaa=baaab⟩	Can Inf
11	5944	⟨a, b \| abbbba=bbbbb⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2789	⟨a, b \| aaaaaaabbaa=1⟩	φ(a) = a, φ(b) = b
11	2801	⟨a, b \| aaaaaabbaaa=1⟩	φ(a) = a, φ(b) = b
11	2825	⟨a, b \| aaaaabbaaaa=1⟩	φ(a) = a, φ(b) = b
11	3304	⟨a, b \| abbbbbbbbba=1⟩	φ(a) = b, φ(b) = a