[GAP Forum] Frobenius group

[Eamonn O'Brien]

Dear Fatemeh:

Lemma 1 of Bertram's 1991 paper in the Israel Journal of Math, vol 75 
(1991) pp. 243-245 offers a characterisation of Frobenius groups which 
is easy to implement and computationally fast. In summary it states:

G is a group with a proper normal subgroup N satisfying k(G) = k(G/N) + 
(k(N) - 1)/[G:N], if and only if G is a Frobenius group with kernel N 
(in which case N is the Fitting subgroup of G).

Here k(H) denotes the number of conjugacy classes of a group H.

Best wishes.

Eamonn