POS-groups with some cyclic Sylow subgroups

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.

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.

Some Sylow Subgroups

The Sylow Subgroups of the Symmetric Groups

The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...

On rational groups with Sylow 2-subgroups of nilpotency class at most 2

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.

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 ...