#283 ⟨a, b | aaaabbba=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element a³ba has infinite order
Inverses of generators:
- a^-1 = a⁴d
- b^-1 = b²c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaabbb⟩
- 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:aaaabbba=1 abcd aaaaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbb=d
aaaaa=c

5 unique, 5 total

Σ	#	Presentation	Properties
8	490	⟨a, b \| aaaaa=bbb⟩	Can Inf
9	1264	⟨a, b \| ababa=bbbb⟩	Can Inf
10	2356	⟨a, b \| abbabba=bbb⟩	Can Inf
11	4301	⟨a, b \| ababababa=bb⟩	Can Inf
11	4357	⟨a, b \| abbbabbba=bb⟩	Can Inf

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

7 total

Σ	#	Presentation	Mapping
8	296	⟨a, b \| aaabbbaa=1⟩	φ(a) = a, φ(b) = b
8	320	⟨a, b \| aabbbbba=1⟩	φ(a) = b, φ(b) = a
11	2819	⟨a, b \| aaaaabababa=1⟩	φ(a) = a, φ(b) = aaaadb
11	2859	⟨a, b \| aaaabababaa=1⟩	φ(a) = a, φ(b) = aaaadb
11	2934	⟨a, b \| aaabababaaa=1⟩	φ(a) = a, φ(b) = aaaadb
11	3171	⟨a, b \| abaaaaaabab=1⟩	φ(a) = a, φ(b) = aaaadb
11	3227	⟨a, b \| ababaaaaaab=1⟩	φ(a) = a, φ(b) = aaaadb