publication . Thesis

Model subgroups of finite soluble groups

Carr, Ben;
Open Access English
  • Country: United Kingdom
In this thesis we begin the study of finite groups possessing a model subgroup, where a model subgroup H of a finite group G is defined to be a subgroup satisfying\ud 〖1H〗^(↑G)=∑_(x∊∕π(G))▒X\ud We show that a finite nilpotent group possesses a model subgroup if and only if it is abelian and that a Frobenius group with Frobenius complement C and Frobenius kernel N possesses a model subgroup if and only if\ud (a) N is elementary abelian of order r".\ud (b) C is cyclic of order (r" — 1 )/(rd — 1), for some d dividing n.\ud (c) The finite field F=Frn has an additive abelian subgroup HF of order rd satisfying NormF/K(HF) =K, where K=Frd.\ud We then go on to conjectur...
arXiv: Mathematics::Group Theory
free text keywords: QA
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