PRIMITIVE SUBGROUPS AND PST-GROUPS

Primitive Actions and Maximal Subgroups of Lie Groups

The classification of the primitive transitive and effective actions of Lie groups on manifolds is a problem dating back to Lie. The classification of the infinite dimensional infinitesimal actions was originally done by Cartan [3] and was made rigorous by some joint work of Guillemin, Quillen and Sternberg [8], whose proof was further simplified by Guillemin [7] recently by using some results ...

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.

Subgroups and cyclic groups

Example 1.2. (i) For every group G, G ≤ G. If H ≤ G and H 6= G, we call H a proper subgroup of G. Similarly, for every group G, {1} ≤ G. We call {1} the trivial subgroup of G. Most of the time, we are interested in proper, nontrivial subgroups of a group. (ii) Z ≤ Q ≤ R ≤ C; here the operation is necessarily addition. Similarly, Q∗ ≤ R∗ ≤ C∗, where the operation is multiplication. Likewise, μn ...

Cyclotomic Swan subgroups and primitive roots

On subgroups of topologized fundamental groups and generalized coverings

‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...