arthrodesis
发表于 2025-3-23 10:12:48
https://doi.org/10.1007/978-3-531-91657-6The notion of generators and relations can be extended from abelian groups to arbitrary groups once we have a nonabelian analogue of free abelian groups. We use the property appearing in Theorem 10.11 as our starting point.
Lignans
发表于 2025-3-23 16:03:13
http://reply.papertrans.cn/16/1556/155600/155600_12.png
鄙视读作
发表于 2025-3-23 21:52:52
http://reply.papertrans.cn/16/1556/155600/155600_13.png
Ingratiate
发表于 2025-3-24 02:15:04
Symmetric Groups and ,-Sets,The definition of group arose from fundamental properties of the symmetric group S.. But there is another important feature of S.: its elements arc functions acting on some underlying set, and this aspect is not explicit in our presentation so far. The notion of . is the appropriate abstraction of this idea.
GIBE
发表于 2025-3-24 02:37:57
The Sylow Theorems,The order of a group . has consequences for its structure. A rough rule of thumb is that the more complicated the prime factorization of |.|, the more complicated the group. In particular, the fewer the number of distinct prime factors in |G|, the more tractible it is. We now study the “local” case when only one prime divides |.|.
免费
发表于 2025-3-24 08:39:06
Normal Series,We begin this chapter with a brief history of the study of roots of polynomials. Mathematicians of the Middle Ages, and probably those in Babylonia, knew the . giving the roots of a quadratic polynomial .(.) = .. + . + .. Setting . transforms .(.) into a polynomial g(.) with no . term:
极深
发表于 2025-3-24 11:38:09
Extensions and Cohomology,A group . having a normal subgroup . can be “factored” into . and .. The study of extensions involves the inverse question: Given . ⊲ . and ., to what extent can one recapture .?
GNAW
发表于 2025-3-24 15:01:36
Abelian Groups,Commutativity is a strong hypothesis, so strong that all finite abelian groups are completely classified. In this chapter, we focus on finitely generated and, more generally, countable abelian groups.
胶水
发表于 2025-3-24 20:39:07
Free Groups and Free Products,The notion of generators and relations can be extended from abelian groups to arbitrary groups once we have a nonabelian analogue of free abelian groups. We use the property appearing in Theorem 10.11 as our starting point.
减弱不好
发表于 2025-3-25 03:12:45
The Word Problem,Novikov, Boone, and Britton proved, independently, that there is a finitely presented group ℬ for which no computer can ever exist that can decide whether an arbitrary word on the generators of ℬ is 1. We shall prove this remarkable result in this chapter.