Simple Current Actions of Cyclic Groups

Simple Current Actions of Cyclic Groups

Rigidity of Trivial Actions of Abelian-by-cyclic Groups

The question of existence and stability of global fixed points for group actions has been studied in many different contexts. In the setting of actions of Lie groups it was shown by Lima [8] that n commuting vector fields on a genus g surface, Σg, of non-zero Euler characteristic have a common singularity. This implies that any action of the abelian Lie group R on Σg has a global fixed point. I...

On the multiplicity-free actions of the sporadic simple groups

We introduce a database containing the character tables of the endomorphism rings of the multiplicity-free permutation modules of the sporadic simple groups, their automorphism groups, their Schur covers, and their bicyclic extensions. We describe the techniques used to compile the data, and present a couple of applications to orbital graphs. MSC: 20C34, 20C40, 20B25, 20B40, 20D08, 05C25.

Finite $p$-groups and centralizers of non-cyclic abelian subgroups

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.