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Title: The order of the group of automorphisms of a finite p-group
Author: Exarchakos, Theodoros
ISNI:       0000 0001 3455 6806
Awarding Body: University of London
Current Institution: Royal Holloway, University of London
Date of Award: 1977
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In this thesis we are mainly concerned with the order of the group A(G) of automorphisms of a finite p-group G.First we determine the order of the group of central automorphisms AC(G) of G in terms of the invariants of its center Z and G/G' , when G is a purely non-abelian group (PN-group). For the general case G = HxK, where H is abelian and K is a PN-group we show thatso that the general case is reduced to that of PN-groups. By using the class c of G we then get These results are used in Chapter 3 to study groups for which |G| divides |A(G)| (LA-groups). It is shown that a non-abelian group G is an LA-group if it has any one of the following properties: (i) order pn, (ii) homocyclic lower central factors and exp G/G1' ≤ |Z|, (iii) cyclic Frattinisubgroup, (iv) certain normal subgroups of maximal class, (v) all two-maximal subgroups abelian, (vi) |G/Z| ≤ p3. In Chapter 4 we find a new bound for the function g(h).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics