منابع مشابه
Homology and Derived P-series of Groups
We prove that groups that are Zp-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings’ 1963 result for the p−lower-central series. In fact we prove a stronger theorem that is analogous to Dwyer’s extensions of Stallings’ results. Similarly, spaces that are Zp-homology equivalent have isomorphic fundamental groups modulo any term of their ...
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In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a solvable completion of a group that is analogous to the Malcev completion, with the role of the lower central series replaced by the...
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In this paper, we first present some properties of lower and upper central series of pair of groups. Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced, and some of the structural properties of the created classes are proved. Moreover some interesting theorems such as Baer Theorem, Bioch Theorem, Hirsh Theorem for pair of groups are generalized...
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We give new information about the relationship between the lowdimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group. Applications are given to detecting when a set of elements of a group generates a subgroup “large enough” to map onto a non-abelian free solvable group, and to...
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فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1965
ISSN: 0021-8693
DOI: 10.1016/0021-8693(65)90017-7