The (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3

Morey, Paul Stephen (2003). The (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3. University of Birmingham. Ph.D.

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Abstract

In this thesis a new characterisation of the (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3 is obtained. It is shown that such an amalgam exists only in the exceptional cases when n=3, 5 or 8. Let C denote the class of all finite groups X of even order and such that O^2(X) is the unique minimal normal subgroup of X. It is the secondary purpose of this thesis to begin an investigation into the structure of the (S_3, C)-amalgams of characteristic 2 and critical distance 3. It is hoped that the results obtained may shed some light on the reason why so few of these amalgams are known to exist.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):