The order of the group of automorphisms of a finite p-group

Exarchakos, Theodoros

(1977)

Exarchakos, Theodoros (1977) The order of the group of automorphisms of a finite p-group.

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Abstract

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,In Chapter 4 we find a new bound for the function g(h)We reduce the previous best bound g(h)

Information about this Version

This is a Accepted version
This version's date is: 1977
This item is not peer reviewed

Link to this Version

https://repository.royalholloway.ac.uk/items/e8bf6775-db19-4093-a80b-804caaf0bf62/1/

Item TypeThesis (Doctoral)
TitleThe order of the group of automorphisms of a finite p-group
AuthorsExarchakos, Theodoros
Uncontrolled KeywordsMathematics; Pure Sciences; A; Automorphisms; Automorphisms; Finite; Group; Order; P
DepartmentsDepartment of Mathematics

Identifiers

ISBN978-1-339-61506-6

Deposited by () on 01-Feb-2017 in Royal Holloway Research Online.Last modified on 01-Feb-2017

Notes

Digitised in partnership with ProQuest, 2015-2016. Institution: University of London, Royal Holloway College (United Kingdom).


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