Sylow \(p\)-subgroup
On supersolvability of finite groups with $\Bbb P$-subnormal subgroups
... Hall subgroup of a group G is P -subnormal. In particular, every Sylow subgroup of G is ...ordered Sylow tower of supersolvable type, in particular, G is ...normal subgroup of the group ...
9
On \(p\)-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups
... a Sylow subgroup of some normal subgroup of G, then we say that P is normally embedded in ...of Sylow p-subgroup, where (|G|, p − 1) = 1, are ...
8
ON p-GROUPS OF ORDER 22n+e,e {0,1} SATISFYING
... A Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G is a maximal p-subgroup of G, ...a subgroup which is a p-group and which is not a proper sub- group of any other ...
5
Serial group rings of finite groups. \(p\)-solvability
... Proof. From the table in [9] we see that there are 123 groups of order ≤ 100 with a nontrivial cyclic 5-Sylow subgroup and 122 of them are 5-solvable. Thus, by Theorem 1 it remains to show that for the ...
16
A note on \(c\)-normal subgroups of finite groups
... all Sylow subgroups of E are cyclic and let P be a Sylow subgroup of E where p is the largest prime divisor of ...characteristic subgroup of ...normal subgroup P ...
11
Characterization of finite groups with some \(S\)-quasinormal subgroups of fixed order
... every subgroup of P of order 2 is normal in G and hence G is 2-nilpotent by Lemma ...a subgroup of P such that |H| = ...a subgroup of P such that H 6 K and |K| = ...a subgroup of G, where R is ...
7
Subgroups, Lattice Structures, and the Number of Sylow -Subgroups for Symmetric Groups P
... the Sylow - subgroups in symmetric groups , n =1, 2,3, 4, 5, 6, 7,8, 9,10 which will lead to a generalization of the number of Sylow -subgroups in any symmetric group and hence coming up with a formula for ...
59
A note on Hall S-permutably embedded subgroups of finite groups
... a subgroup of G such that H/(N ∩ X) is a Hall π-subgroup of X/N ∩ ...proper subgroup of ...the Sylow p-subgroups of N are Sylow p-subgroups of ...every Sylow subgroup of G ...
7
Criterions of supersolubility of some finite factorizable groups
... cyclic subgroup of A X-permutes with every Sylow subgroup of B and if in return every primary cyclic subgroup of B X -permutes with every Sylow subgroup of A where X = F (G) is ...
10
The double transitivity of a class of permutation groups
... every abelian group of composite order which has at least one cyclic Sylow subgroup is a B-group.. generalized the Burnside result.[r] ...
46
Groups with the same orders of Sylow normalizers as the Mathieu groups
... Proof. By Lemma 3.1, G has a normal series 1 H K G such that K/H is a simple group, 11 is a divisor of | K/H | , and | G/K | divides 5. We claim that | H | is a divisor of 5. Since 11 divides | K/H | , we have 11 | H | . ...
5
A probabilistic version of a theorem of lászló kovács and hyo-seob sim
... Sylow 2-subgroup of G. We would need a similar result, using a subgroup of odd index instead of a Sylow 2-subgroup. In the remaining part of this section we want to discuss a question ...
6
\(\mathbf{S}\)-Embedded subgroups in finite groups
... A subgroup H of a group G is said to be semipermutable ...every subgroup (resp. Sylow subgroup) K of G such that (|H|, |K |) = ...S-semipermutable subgroup of a group need not be ...
8
Finite groups with cyclic Sylow subgroups for all odd primes
... cyclic Sylow 2-subgroup is non-sinple and it follows from the Feit-Thonpson Theorem that it is even ...whose Sylow 2-subgroups are non-cyclic, A definition is appropriate ...
115
Sylow like theorems for $V(\mathbb{Z}G)$
... Even for groups of order six SIP is an open problem. If one restricts himself to a specific class of groups (e.g. to the case that G soluble) then much more is known. This show the results of A. Weiss [44], mentioned ...
11
Nilpotent L-subgroups and the Set Product of L-subsets
... Since the level subsets of η are normal subgroups of G, η is a normal L-subgroup of G. Similarly, it can be seen that θ and φ are also normal L−subgroups of G and hence of µ. Now η is a nilpotent L-subgroup ...
17
Vol 2, No 5 (2011)
... of Sylow 2-subgroup of symmetric groups S n is studied by ...that Sylow 2-subgroup is ...of Sylow subgroups (also called the Sylow numbers) is due to Professor Jiping Zhang ...of ...
5
The Maschke property for the Sylow $p$-sub\-groups of the symmetric group $S_{p^n}$
... Remark 4.5. The following result is used in the proofs of Theorem 1.3 and Proposition 5.1. Special cases of this result have been proved before: The case where p is odd and N is a partition subgroup is due to Weir ...
24
On metacyclic subgroups of finite groups
... In the second part of the article, we are concerned with the influence of 2-generator subgroups on the structure of a group. The basic idea behind the results is the following: assume that a group G has 2-generator ...
5
Sylow multiplicities in finite groups
... Recall that for any finite group G the product of all subgroups of G which are both normal and solvable is a normal and solvable subgroup, called the solvable radical of G. The solvable radical of G will be ...
8