辫群是一种非交换的无限群，该群中有许多困难问题是不可解的，如字问题、共轭问题和根问题等，利用这些困难问题可以去设计一些密码协议。
The braid group is infinite non-commutative group, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.
到目前为止，对于交换群和可解群，CI -性的研究已有了相当彻底的结果。
Concerning the Abelian groups and solvable groups, the researches on CI-properties had rather thorough results until now.
本文第四部分3.4，主要讨论了交换子群对有限群可解性的影响，得到了有限群可解的若干充分条件。
In the last section, namely 3.4, we mainly discuss how Abelian subgroups influent the solvability of finite groups, so we obtain some sufficient conditions of solvable groups.
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