I have had many guppies together in a ten gallon and now in a 20 gallon and have not had any trouble with fighting. They all seem to get along very well together. The problem is when you have alot of males and only a few females as the males will pester the girls non stop and both sexes get stressed out. If you were thinking of breeding them, I would only add one male. If you have lots of hiding places with 6 girls and a male guppy you will have a tank full in no time.
Do you have any other fish in the tank? They could just be a little stressed because the tank is a bit small as guppies can be a pretty active fish.
To the poster before me you want about a 2f to 1m ratio or maybe 3f to 1m at most or the male will wear himself out and get stressed out from trying to mate with so many females and probably not make it.
EDIT: and females are better to keep together as males are more territorial and such.
Females will fight rarely. Usually only when a female is pregnant and you have a dominant female in the tank, the dominant one will harrass the lower level pregnant guppy. But doesn't happen all the time. However 6 guppies in a 10g is a bit ovecrowded. I'd knock it back to 4 if you can. Also, even if you don't have a male guppy now, if they have been in contact with one within the past few months they could still have sperm stored and be pregnant. If you have nice hidey holes you'll end up with a bunch of babies and an extremely over crowded tank.
Edit: Males are prettier, but they do occasionally fight. They're more likely to fight if you don't have females to go around.
My tip is buy females, and buy them from a store that keeps the males and females separated.
I've never had an issue with females fighting with one another. If you do put both males and females in there, it helps to have the females all basically the same size, if there is one much larger then the male(s) will gravitate towards it in particular.
If you don't have a weak spot for baby fish then dont leave many hiding places (floating grass/moss) and just let nature work itself out.