*PM : classification of finite nilpotent groups, id = 3755-- WP guess : classification of finite nilpotent groups-- Status:
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*PM : classification of finite nilpotent groups, id = 3755-- WP guess : classification of finite nilpotent groups-- Status:
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A Riemannian manifold is called a "'homogeneous nilmanifold "'if there exist a nilpotent group of isometries acting transitively on it.
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His thesis, " Zeta functions of torsion-free finitely generated nilpotent groups ", was written under the direction of Dan Segal.
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A Carter subgroup is a maximal nilpotent subgroup, because of the normalizer condition for nilpotent groups, but not all maximal nilpotent subgroups are Carter subgroups.
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An earlier result of Joseph A . Wolf showed that if " G " is a finitely generated nilpotent group, then the group has polynomial growth.
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The nilpotent groups whose center is cyclic and derived subgroup has order " p " and whose conjugacy classes are at most countably infinite are classified in.
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Since the Fitting subgroup of a finite solvable group contains its own centralizer, this gives a method of understanding finite solvable groups as faithful automorphism groups of nilpotent groups.
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These series can be constructed for any group, and if a group has a central series ( is a nilpotent group ), these procedures will yield central series.
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Beyond Gromov's theorem one can ask whether there exists a gap in the growth spectrum for finitely generated group just above polynomial growth, separating virtually nilpotent groups from others.
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