I came across this usage when reading New York's Bloodiest Week from AMERICAN HERITAGE, an article on the 1863 draft riot in NY city,
The mob was to make its last stand on the East Side. Five thousand desperate men attacked elements of the Seventh Regiment on Second Avenue in what the Times labeled “the most sanguinary fight of the whole riot.” Bullets and bricks from the rooftops killed fifteen soldiers before another 700 troops arrived to clear the avenue with artillery and bayonet.
According to Dictionary.com, 'element' means 'a component or constituent of a whole or one of the parts into which a whole may be resolved by analysis'. So does it here refer to the 'individual soldiers' making up the 'regiment' or it bears other connotations?