Non-Abelian homology of groups

被引：9

作者：

Inassaridze, H ^{[1
]}

Inassaridze, N ^{[1
]}

机构：

[1] Georgian Acad Sci, A Razmadze Math Inst, GE-380093 Tbilisi, Georgia

来源：

K-THEORY | 1999年 / 18卷 / 01期

关键词：

tensor product; derived functors; non-Abelian group homology;

D O I：

10.1023/A:1007881911578

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New descriptions of non-Abelian group homology in terms of derived functors are given and the Mayer-Vietoris sequence is constructed. Sufficient conditions are established for non-Abelian homology groups of dimension greater than or equal to 2 to be finitely generated, finite, p-groups, torsion groups or groups of exponent q. Some formulas for the second and third non-Abelian homology of groups are obtained.

引用

页码：1 / 17

页数：17

共 19 条

[1] VANKAMPEN THEOREMS FOR DIAGRAMS OF SPACES [J].

BROWN, R ;

LODAY, JL .

TOPOLOGY, 1987, 26 (03) :311-335

[2] SOME COMPUTATIONS OF NON-ABELIAN TENSOR-PRODUCTS OF GROUPS [J].

BROWN, R ;

JOHNSON, DL ;

ROBERTSON, EF .

JOURNAL OF ALGEBRA, 1987, 111 (01) :177-202

[3]

BROWN R, 1984, CR ACAD SCI I-MATH, V298, P353

[4]

Dennis R. K, 1976, SEARCH NEW HOMOLOGY

[5] ON THE GROUPS H(II, N) .2. METHODS OF COMPUTATION [J].

EILENBERG, S ;

MACLANE, S .

ANNALS OF MATHEMATICS, 1954, 60 (01) :49-139

[6] HOMOLOGY THEORIES FOR MULTIPLICATIVE SYSTEMS [J].

EILENBERG, S ;

MACLANE, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 71 (SEP) :294-330

[7] NON-ABELIAN COHOMOLOGY AND HOMOLOGY OF GROUPS [J].

GUIN, D .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1988, 50 (02) :109-137

[8]

Inassaridze H., 1997, Non-Abelian Homological Algebra and Its Applications. Mathematics and its Applications

[9]

INASSARIDZE H, 1975, MATH USSR SB, V27, P339

[10] Nonabelian tensor products and Nonabelian homology of groups [J].

Inassaridze, N .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1996, 112 (02) :191-205

← 1 2 →