English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

There are four groups $G$ fitting into a short exact sequence $ 1\rightarrowSL(2,5)\rightarrow G\rightarrow C_2\rightarrow 1, $ where $SL(2,5)$ is thespecial linear group of $(2\times 2)$-matrices with entries in the field offive elements. Except for the direct product of $SL(2,5)$ and $C_2$, there aretwo other semidirect products of these two groups and just one non-semidirectproduct $SL(2,5).C_2$, considered in this paper. It is known that each finitenonsolvable group can act on spheres with arbitrary positive number of fixedpoints. Clearly, $SL(2,5).C_2$ is a nonsolvable group. Moreover, it turns outthat $SL(2,5).C_2$ possesses a free representation and as such, can potentiallyact pseudofreely with nonempty fixed point set on manifolds of arbitrarilylarge dimension. We prove that $SL(2,5).C_2$ cannot act effectively with oddnumber of fixed points on low-dimensional spheres. In the special case ofeffective one fixed point actions, we are able to exclude a wider class ofspheres. Moreover, we prove that specific pseudofree one fixed point actions of$SL(2,5).C_2$ on spheres do not exist.

Exclusions of smooth actions on spheres of the non-split extension of $C_2$ by $SL(2,5)$