Displaying similar documents to “On S -quasinormal and c -normal subgroups of a finite group”

The influence of weakly-supplemented subgroups on the structure of finite groups

Qingjun Kong, Qingfeng Liu (2014)

Czechoslovak Mathematical Journal

Similarity:

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In the paper it is proved that a finite group G is p -nilpotent provided p is the smallest prime number dividing the order of G and every minimal subgroup of P ∩ G ' is weakly-supplemented in N G ( P ) , where P is a Sylow p -subgroup of G . As applications, some interesting results with weakly-supplemented minimal subgroups of P ∩ G ' are obtained.

On weakly s -permutably embedded subgroups

Changwen Li (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Suppose G is a finite group and H is a subgroup of G . H is said to be s -permutably embedded in G if for each prime p dividing | H | , a Sylow p -subgroup of H is also a Sylow p -subgroup of some s -permutable subgroup of G ; H is called weakly s -permutably embedded in G if there are a subnormal subgroup T of G and an s -permutably embedded subgroup H s e of G contained in H such that G = H T and H ∩ T ≤ H s e . We investigate the influence of weakly s -permutably embedded subgroups on the p -nilpotency and p -supersolvability...

Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements

Changguo Shao, Qinhui Jiang (2014)

Czechoslovak Mathematical Journal

Similarity:

Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups G whose set of numbers of subgroups of possible orders n ( G ) has exactly two elements. We show that if G is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then G has a normal Sylow subgroup of prime order and G is solvable. Moreover, as an application we give a detailed description of non-nilpotent...

On some soluble groups in which U -subgroups form a lattice

Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The article is dedicated to groups in which the set of abnormal and normal subgroups ( U -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.