اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe class $mathcal{MN}$ of groups in which all maximal subgroups are normal
125
0
0.0
(
0
)
تأليف
Aglaia Myropolska
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate the class $mathcal{MN}$ of groups with the property that all maximal subgroups are normal. The class $mathcal{MN}$ appeared in the framework of the study of potential counter-examples to the Andrews-Curtis conjecture. In this note we give various structural properties of groups in $mathcal{MN}$ and present examples of groups in $mathcal{MN}$ and not in $mathcal{MN}$.
قيم البحث
اقرأ أيضاً
It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian groups.
In 1933 B.~H.~Neumann constructed uncountably many subgroups of ${rm SL}_2(mathbb Z)$ which act regularly on the primitive elements of $mathbb Z^2$. As pointed out by Magnus, their images in the modular group ${rm PSL}_2(mathbb Z)cong C_3*C_2$ are ma
ximal nonparabolic subgroups, that is, maximal with respect to containing no parabolic elements. We strengthen and extend this result by giving a simple construction using planar maps to show that for all integers $pge 3$, $qge 2$ the triangle group $Gamma=Delta(p,q,infty)cong C_p*C_q$ has uncountably many conjugacy classes of nonparabolic maximal subgroups. We also extend results of Tretkoff and of Brenner and Lyndon for the modular group by constructing uncountably many conjugacy classes of such subgroups of $Gamma$ which do not arise from Neumanns original method. These maximal subgroups are all generated by elliptic elements, of finite order, but a similar construction yields uncountably many conjugacy classes of torsion-free maximal subgroups of the Hecke groups $C_p*C_2$ for odd $pge 3$. Finally, an adaptation of work of Conder yields uncountably many conjugacy classes of maximal subgroups of $Delta(2,3,r)$ for all $rge 7$.
In this paper, we study a group in which every 2-maximal subgroup is a Hall subgroup.
The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CA-group
. It is shown that G has a normal open subgroup N which is either abelian or pro-p. Further, a rather detailed information about the finite quotient G/N is obtained.
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normali
ser, and show that its properties reflect the global structure of the ambient group.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
