On maximal cyclic subgroups in finite p-groups |
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Authors: | Zvonimir Janko |
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Institution: | (1) Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany |
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Abstract: | In this note we consider finite noncyclic p-groups G all of whose maximal cyclic subgroups X satisfy one of the following two properties.
(a) If each subgroup H of G containing X properly is nonabelian, then p = 2 and G is generalized quaternion.
(b) If X is contained in exactly one maximal subgroup of G, then G is metacyclic.
This solves the problems Nr.1541 and Nr. 1594 from 1]. |
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Keywords: | Finite p-groups powerful p-groups metacyclic p-groups |
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