نتایج جستجو برای: frattini extension
تعداد نتایج: 149273 فیلتر نتایج به سال:
Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.
*Renier J. Brentjens,1-3 *Isabelle Rivière,1-4 Jae H. Park,1,2 Marco L. Davila,1,2 Xiuyan Wang,2-4 Jolanta Stefanski,2-4 Clare Taylor,2-4 Raymond Yeh,1,2 Shirley Bartido,2,3 Oriana Borquez-Ojeda,2-4 Malgorzata Olszewska,2-4 Yvette Bernal,1 Hollie Pegram,1,2 Mark Przybylowski,2-4 Daniel Hollyman,2-4 Yelena Usachenko,1,2 Domenick Pirraglia,2-4 James Hosey,2-4 Elmer Santos,3,5 Elizabeth Halton,1 P...
The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T.Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E....
Let Γg,b denote the orientation-preserving Mapping Class Group of a closed orientable surface of genus g with b punctures. For a group G let Φf (G) denote the intersection of all maximal subgroups of finite index in G. Motivated by a question of Ivanov as to whether Φf (G) is nilpotent when G is a finitely generated subgroup of Γg,b, in this paper we compute Φf (G) for certain subgroups of Γg,b...
For a finite group G and an inverse-closed generating set C of G, let Aut(G;C) consist those automorphisms which leave invariant. We define Aut(G;C)-invariant normal subgroup Φ(G;C) has the property that, for any generators if we remove from it all elements Φ(G;C), then remaining is still G. The contains Frattini Φ(G) but inclusion may be proper. Cayley graph Cay(G,C) edge-transitive acts trans...
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