NETMaths
Log inStart free

Is this true?

If d divides |G| then G has a subgroup of order d

No — it is false.

The counterexample

has order 12 but no subgroup of order 6

The kind of mistake this is

Finite-dimensional intuition

Something true in ℝⁿ, or in a nice space, assumed in general.

Drill statements like this
groups

Others that fail the same way

From Groups › Subgroups, cosets, Lagrange, cyclic groups

ShareWhatsAppTelegram