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- W172978852 abstract "The generation problems are very interesting in the theory of finite groups. These problems can often be reduced to problems on the generators of p-groups. This has led to an increasing interest on the problems of generation in and on the study of classes of in which generators satisfy some precise conditions. In particular, it is very interesting the class of finite G with the property that the rank of G is equal to the number of generators of G (i.e. the number of generators of every subgroup of G is smaller than or equal to the number of generators of G). For instance, the abelian, the modular and the powerful belong to this class. Also the monotone lie in this class. We recall here the definition of monotone p-groups.Definition: Let G be a group. We denote with d(G) the number of generators of G.A p-group G is monotone if for every H and K subgroups of G with H contained in K, we have that d(H) is smaller than or equal to d(K). The class of monotone was introduced by A. Mann during the 1985 Saint Andrews Conference. In the paper The number of generators of finite p-groups published in 2005, Mann studies the monotone and classifies the monotone for p odd.When p=2, Mann does not classify the monotone 2-groups, but he gives some remarkable properties. For instance, he proves that a 2-group G is monotone if and only if the 2-generated subgroups of G are metacyclic.In this thesis, the monotone 2-groups are studied and completely determined." @default.
- W172978852 created "2016-06-24" @default.
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- W172978852 date "2009-06-30" @default.
- W172978852 modified "2023-09-27" @default.
- W172978852 title "Monotone 2-Groups" @default.
- W172978852 hasPublicationYear "2009" @default.
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