Alperin [I] has recently introduced a fundamental method for conjugating from one p-Sylow subgroup Q of a finite group G to a second p-Sylow subgroup Pin a series of steps. The importance of this is that it provides information concerning the conjugacy in G of subsets of P, that is, fusion of subsets of P. In certain situations it is possible to extend these results to the case of conjugate p-s...

Given a set r of permutations of an n-set, let G be the group of permutations generated by f. If p is a prime, a Sylow p-subgroup of G is a subgroup whose order is the largest power of p dividing IGI. For more than 100 years it has been known that a Sylow p-subgroup exists, and that for any two Sylow p-subgroups PI, P, of G there is an element go G such that Pz = g-‘PI g. We present polynomial-...

‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

Alperin [1] has recently introduced a fundamental method for conjugating from one p-Sylow subgroup Q of a finite group G to a second p-Sylow subgroup P in a series of steps. The importance of this is that it provides information concerning the conjugacy in G of subsets of P, that is, fusion of subsets of P. In certain situations it is possible to extend these results to the case of conjugate p-...

We explore 2-Sylow theory in groups of finite Morley rank, developing the language necessary to begin to understand the structure of such groups along the way, and culminating in a proof of a theorem of Borovik and Poizat that all Sylow 2-subgroups are conjugate in a group of finite Morley

subgroups cannot involve two operators whose orders are powers of prime numbers and whose product has an order which is a power of another prime number. In particular, a solvable group cannot involve two such operators. The second question to which we referred above is as follows: Is there a group which is not the product of some one of its possible sets of non-conjugate Sylow subgroups? I t is...

In finite group theory, one of the most influential ideas is the notion of Sylow p-subgroup. It was used to classify many groups of finite order. Despite original intentions to use it with finite group, it was extended to study Lie group, which inspires recent development in p-compact group. Here, we will discuss some aspects of Sylow’s Subgroup Theorem. In particular, the focus is on a finite ...

In this paper, we prove the p-nilpotency of a finite group with assumption that some subgroups of Sylow subgroup are weakly s-semipermutable subgroups in the normalizer of Sylow subgroups. Our results unify and generalize some earlier results. Mathematics Subject Classification: 20D10, 20D15