The number of possible isomers with side chains increases as the number of carbon aroms increases. The side chain can be considered as an alkane molecule that has lost a hydrogen atom. The fragment of the alkane that forms the side chain is called an alkyl group.
What does this even mean???
wunderkind52 beat me to it, but nevermind, I'll still contribute my two cents:
An isomer of a molecule is a molecule with the same molecular formula, but a different structural formula (so essentially the same type and number of elements are present, but the atoms are arranged differently). As the number of carbon atoms in the carbon-backbone of an organic molecule increases, there becomes an increased number of ways that the atoms can be arranged, while still giving the same molecular formula (however the structural formula will have changed).
In forming isomers, often part of the original molecule becomes attached elsewhere as sidechains known as alkyl groups. So for example an alkyl group derived from methane (CH4) has one less hydrogen atom than methane, thus has a formula of CH3 and is called a methyl group.
Hope that cleared some of your doubts up!
