اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSchreiers formula for Prosupersolvable groups
40
0
0.0
(
0
)
تأليف
Mark Shusterman
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We classify the finitely generated prosupersolvable groups that satisfy Schreiers formula for the number of generators of open subgroups.
قيم البحث
اقرأ أيضاً
This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $nleq 7$ which are Hurwitz, where $F$ is an alge
braically closed field. For the groups $G_2(q)$, $qgeq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators.
The famous Tits alternative states that a linear group either contains a nonabelian free group or is soluble-by-(locally finite). We study in this paper similar alternatives in pseudofinite groups. We show for instance that an $aleph_{0}$-saturated p
seudofinite group either contains a subsemigroup of rank $2$ or is nilpotent-by-(uniformly locally finite). We call a class of finite groups $G$ weakly of bounded rank if the radical $rad(G)$ has a bounded Prufer rank and the index of the sockel of $G/rad(G)$ is bounded. We show that an $aleph_{0}$-saturated pseudo-(finite weakly of bounded rank) group either contains a nonabelian free group or is nilpotent-by-abelian-by-(uniformly locally finite). We also obtain some relations between this kind of alternatives and amenability.
Let PC be the group of bijections from [0, 1[ to itself which are continuous outside a finite set. Let PC be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of PC vanishes. That is, the quotient map
PC $rightarrow$ PC splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from PC to Z 2Z. Then we use this signature to list normal subgroups of every subgroup G of PC which contains S fin and such that G, the projection of G in PC , is simple.
We study a random group G in the Gromov density model and its Cayley complex X. For density < 5/24 we define walls in X that give rise to a nontrivial action of G on a CAT(0) cube complex. This extends a result of Ollivier and Wise, whose walls could
be used only for density < 1/5. The strategy employed might be potentially extended in future to all densities < 1/4.
The branching theorem expresses irreducible character values for the symmetric group $S_n$ in terms of those for $S_{n-1}$, but it gives the values only at elements of $S_n$ having a fixed point. We extend the theorem by providing a recursion formula
that handles the remaining cases. It expresses these character values in terms of values for $S_{n-1}$ together with values for $S_n$ that are already known in the recursive process. This provides an alternative to the Murnaghan-Nakayama formula.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
