- #1
Firepanda
- 430
- 0
Show that the Cardinality of a set which doesn't include inverse elements from a group G is always even.
So the set with all g in G, which includes no inverse elements from G. (g=!g^-1)
I can get this in every example I've done, checking mainly with dihedral groups, it's always been true but I can't find a pattern.
I know that the neutral element can't be in the set, so that's one down, then I thought maybe halfing it, which is wrong I know, as I kept finding cases where the element itself was it's own inverse.
I've really no idea where to go from here.
So the set with all g in G, which includes no inverse elements from G. (g=!g^-1)
I can get this in every example I've done, checking mainly with dihedral groups, it's always been true but I can't find a pattern.
I know that the neutral element can't be in the set, so that's one down, then I thought maybe halfing it, which is wrong I know, as I kept finding cases where the element itself was it's own inverse.
I've really no idea where to go from here.