Universiteit Leiden

nl en


Intense automorphisms of finite groups

In this thesis we classify the pairs (p,G), where p is a prime number and G is a finite p-group possessing an intense automorphism, i.e. an automorphism that sends each subgroup of G to a G-conjugate, that is non-trivial and whose order is coprime to p.

Mima Stanojkovski
05 september 2017
Thesis in Leiden Repository

The background image of the cover of this thesis has been drawn by the author. The vertices of the illustrated graph represent equivalence classes of subgroups of MC(3), as defined in Section 9.2, with respect to the equivalence relation H ∼ K if and only if, for each j ∈ {1, 2, 3, 4}, the j-th widths, as defined in Section 2.3, of H and K in MC(3) are the same. An edge is drawn between two vertices if there are representatives H and K of the given vertices such that H is contained in K with index 3 or vice versa. The color of each vertex is determined by the number of conjugates in MC(3) of any representative of the equivalence class associated to the vertex. Subgroups corresponding to white, blue, red, and yellow vertices have respectively 1, 3, 9, and 27 conjugates in MC(3)