In Australian usage, wife beater is slang for the underwear item, called a vest in the UK and a singlet here, worn as an outer (and only) top garment. A tank top is a similar garment, usually coloured rather than plain white or navy blue, designed to be worn instead of a tee shirt. Such a garment would usually be made of cotton. A sleeveless sweater (or jumper here) is usually made of wool, knitted and worn over a collared shirt. Sleeveless jumpers have been around, and called that, for as long as I can remember, although less common now. Fair Isle patterns were popular in the 40s and 50s.