Commanders providing classes on Nelson's essence (8)

'commanders' is the definition.
The definition and answer can be both people as well as being plural nouns.
Maybe they are linked in a way I don't understand?

'classes on nelson's essence' is the wordplay.
'classes' becomes 'genera' (more than one genus - a class or category).
'on' means one lot of letters go next to another.
'essence' says to take the centre (essence can mean the core of something).
The centre of 'nelson' is 'ls'.
'genera'+'ls'='GENERALS'

'providing' acts as a link.

Can you help me to learn more?