Vladimir Lukyanenko - Academia.edu (original) (raw)
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Papers by Vladimir Lukyanenko
Acta Mathematica Hungarica, Mar 16, 2015
Let G be a nite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permut... more Let G be a nite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that |Q|, |H| = 1 and |H|, |Q G | = 1; (2) H is weakly τ-quasinormal in G if G has a subnormal subgroup T such that HT = G and T ∩ H H τ G , where H τ G is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. Our main result here is the following. Let F be a saturated formation containing all supersoluble groups and let X E be normal subgroups of a group G such that G/E ∈ F. Suppose that every non-cyclic Sylow subgroup P of X has a subgroup D such that 1 < |D| < |P | and every subgroup H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is non-Abelian) not having a supersoluble supplement in G is weakly τ-quasinormal in G. If X is either E or F * (E), then G ∈ F.
Rendiconti del Seminario Matematico della Università di Padova, 2010
Let H be a subgroup of a finite group G. We say that H is t-quasinormal in G if HP PH for all Syl... more Let H be a subgroup of a finite group G. We say that H is t-quasinormal in G if HP PH for all Sylow p-subgroups P of G such that (jHj; p) 1 and (jHj; jP G j) T 1. In this article, finite groups in which t-quasinormality is a transitive relation are described.
Asian-European Journal of Mathematics, 2008
Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH... more Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-quasinormal in G. Then we say that H is nearly S-quasinormal in G if G has an S-quasinormal subgroup T such that HT = G and T ∩ H ≤ HsG. Our main result here is the following theorem. Let [Formula: see text] be a saturated formation containing all supersoluble groups and G a group with a normal subgroup E such that [Formula: see text]. Suppose that every non-cyclic Sylow subgroup P of E has a subgroup D such that 1 < |D| < |P| and all subgroups H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is a non-abelian 2-group) having no supersoluble supplement in G are nearly S-quasinormal in G. Then [Formula: see text].
Our main result here is the following theorem: Let G = AT, where A is a Hall π-subgroup of G and ... more Our main result here is the following theorem: Let G = AT, where A is a Hall π-subgroup of G and T is p-nilpotent for some prime p ∉ π, let P denote a Sylow p-subgroup of T and assume that A permutes with every Sylow subgroup of T. Suppose that there is a number pk such that 1 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; pk &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; |P| and A permutes with every subgroup of P of order pk and with every cyclic subgroup of P of order 4 (if pk = 2 and P is non-abelian). Then G is p-supersoluble.
Acta Mathematica Hungarica, Mar 16, 2015
Let G be a nite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permut... more Let G be a nite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that |Q|, |H| = 1 and |H|, |Q G | = 1; (2) H is weakly τ-quasinormal in G if G has a subnormal subgroup T such that HT = G and T ∩ H H τ G , where H τ G is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. Our main result here is the following. Let F be a saturated formation containing all supersoluble groups and let X E be normal subgroups of a group G such that G/E ∈ F. Suppose that every non-cyclic Sylow subgroup P of X has a subgroup D such that 1 < |D| < |P | and every subgroup H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is non-Abelian) not having a supersoluble supplement in G is weakly τ-quasinormal in G. If X is either E or F * (E), then G ∈ F.
Rendiconti del Seminario Matematico della Università di Padova, 2010
Let H be a subgroup of a finite group G. We say that H is t-quasinormal in G if HP PH for all Syl... more Let H be a subgroup of a finite group G. We say that H is t-quasinormal in G if HP PH for all Sylow p-subgroups P of G such that (jHj; p) 1 and (jHj; jP G j) T 1. In this article, finite groups in which t-quasinormality is a transitive relation are described.
Asian-European Journal of Mathematics, 2008
Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH... more Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-quasinormal in G. Then we say that H is nearly S-quasinormal in G if G has an S-quasinormal subgroup T such that HT = G and T ∩ H ≤ HsG. Our main result here is the following theorem. Let [Formula: see text] be a saturated formation containing all supersoluble groups and G a group with a normal subgroup E such that [Formula: see text]. Suppose that every non-cyclic Sylow subgroup P of E has a subgroup D such that 1 < |D| < |P| and all subgroups H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is a non-abelian 2-group) having no supersoluble supplement in G are nearly S-quasinormal in G. Then [Formula: see text].
Our main result here is the following theorem: Let G = AT, where A is a Hall π-subgroup of G and ... more Our main result here is the following theorem: Let G = AT, where A is a Hall π-subgroup of G and T is p-nilpotent for some prime p ∉ π, let P denote a Sylow p-subgroup of T and assume that A permutes with every Sylow subgroup of T. Suppose that there is a number pk such that 1 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; pk &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; |P| and A permutes with every subgroup of P of order pk and with every cyclic subgroup of P of order 4 (if pk = 2 and P is non-abelian). Then G is p-supersoluble.