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OD-characterization of alternating groupsA p + d

100%

Yang Y., Liu S., Zhang Z.

Open Mathematics

2017

tom 15

nr 1

1090-1098

Let An be an alternating group of degree n. Some authors have proved that A10, A147 and A189 cannot be OD-characterizable. On the other hand, others have shown that A16, A23+4, and A23+5 are OD-characterizable. We will prove that the alternating groups Ap+d except A10, are OD-characterizable, where p is a prime and d is a prime or equals to 4. This result generalizes other results.

Maximal subgroups and PST-groups

84%

Ballester-Bolinches A., Beidleman J., Esteban-Romero R., Pérez-Calabuig V.

Open Mathematics

2013

tom 11

nr 6

1078-1082

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

Ograniczanie wyników

2 Open Mathematics

1 Ballester-Bolinches A.

1 Beidleman J.

1 Esteban-Romero R.

1 Liu S.

1 Pérez-Calabuig V.

1 Yang Y.

1 Zhang Z.

1 2017

1 2013

Wyniki wyszukiwania

OD-characterization of alternating groupsA p + d

Maximal subgroups and PST-groups