NETMaths
Log inStart free

Is this true?

Converse of Lagrange: d | |G| ⇒ subgroup of order d

No — it is false.

The counterexample

has no subgroup of order 6

The kind of mistake this is

Property not inherited

A property assumed to pass to subobjects, quotients, or through a chain. It does not.

Drill statements like this
groups

Others that fail the same way

From Groups › Normal subgroups, quotients, isomorphism theorems

ShareWhatsAppTelegram