Finiteness conditions on subnormal and ascendant abelian subgroups
نویسندگان
چکیده
منابع مشابه
Finiteness Conditions on Subgroups and Formal Language Theory
We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and...
متن کاملFiniteness conditions on characteristic closures and cores of subgroups
We characterise groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p in which...
متن کاملConnected transversals to subnormal subgroups
Subnormal subgroups possessing connected transversals are briefly discussed.
متن کاملOn the Avalanche-finiteness of Abelian Sandpiles
We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O (
متن کاملFinite Groups Whose «-maximal Subgroups Are Subnormal
Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1968
ISSN: 0021-8693
DOI: 10.1016/0021-8693(68)90084-7