Some Examples of Free Actions on Products of Spheres
نویسنده
چکیده
If G1 and G2 are finite groups with periodic Tate cohomology, then G1 × G2 acts freely and smoothly on some product S n × S.
منابع مشابه
Examples of Free Actions on Products of Spheres
We construct a non-abelian extension Γ of S by Z/3 × Z/3, and prove that Γ acts freely and smoothly on S × S. This gives new actions on S × S for an infinite family P of finite 3-groups. We also show that any finite odd order subgroup of the exceptional Lie group G2 admits a free smooth action on S × S. This gives new actions on S×S for an infinite family E of finite groups. We explain the sign...
متن کاملA new notion of rank for finite supersolvable groups and free linear actions on products of spheres
For a finite supersolvable group G, we define the saw rank of G to be the minimum number of sections Gk − Gk−1 of a cyclic normal series G∗ such that Gk − Gk−1 owns an element of prime order. The axe rank of G, studied by Ray [10], is the minimum number of spheres in a product of spheres admitting a free linear action of G. Extending a question of Ray, we conjecture that the two ranks are equal...
متن کاملCyanation and bromination of electron-rich aromatics by BrCN under solvent-free conditions catalyzed by AlCl3: A new examples of Beckmann-type rearrangement
A convenient route for cyanation and bromination of some electron-rich aromatics (anisole, 1,3-dimethoxybenzene, 1,4-dimethoxybenzene, 1,3,5-trimethoxybenzene and β-naphthol) by BrCN in the presence of aluminum trichloride (AlCl3), as catalyst, by grinding method under solvent-free conditions at room temperature to 60 °C was described in good yield. The structures of all obtained products were ...
متن کاملExtending Free Cyclic Actions on Spheres
Connolly and Geist have reduced the problem of determining which free cyclic actions on spheres extend to free actions of specified supergroups to a problem involving a certain transfer map. In this note we develop some algebraic tools for calculating the transfer and show that some cyclic actions do not extend to certain supergroups.
متن کاملCyclic Group Actions on Contractible 4-manifolds Nima Anvari and Ian Hambleton
There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that smooth free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which the actions extend locally linearly but not smoothly.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006