当且仅当

One of the cases was showed in theorem 4.18: finite group G is solvable if and only if Sec is nilpotent for every maximal subgroup At without prime index in G.

在本文中作者将要证明：G可解当且仅当对G中的任意极大子群M，或者I中存在极大元C使C/K幂零并且其Sylow2-子群的幂零类≤2，或者Sec为2-闭。

A string is true if and only if its length is non-zero.

一个字符串当且仅当它的长度不为0是，表达式的值为真。

Positive semi-definite matrices are positive definite if and only if they are nonsingular.

正半定矩阵是正定的，当且仅当它们是非奇异矩阵。

To examine the topological space theory by nonstandard analysis, the nonstandard characteristics of ideals convergence is given in the enlargement model.

为了用非标准分析方法进一步研究拓扑空间，在扩大模型下，对理想收敛的基本理论进行了非标准刻画：设X是拓扑空间，I是X中的理想，I收敛于点x，当且仅当v v 。

A basic fact about sets is that there are two sets only when their memberships differ. The membership of the set of things that are phlogiston is exactly the same as the membership of the set of things that are Devil-dealing Salem witches. In each case, there are none. So in each case the set of instances is the set with no members, the null set.

按集合观，不承认这里有不同的共相，因为基础事实是，两个集合不同当且仅当成员不同，而这两个集合是相同的，因为都是没有成员的集合，即空集。

If and only if p is a minimal prime of a principal ideal.

当且仅当p是一个主理想上的极小素理想。

It is very difficult to discrimnate a natural number to be a prime number by J Wilson s theorem This paper presents another method for discriminating prime number .

本文给出关于质数一个判定准则：数P为质数，当且仅当P不能表示为四个自然数之和，使其中的两数之积等于其余两数之积

The main resul ts show that any pair of pure finite epistemic states are quasi skep tically equivalent if and only if their par-images are similar.

利用有限子语言在原语言上的归约，得到如下的表示定理：任两个纯的有限认知态是拟怀疑等价的，当且仅当它们作用算子 par后结构相似。

A magma ''Q'' is a quasigroup precisely when these operators are bijective. The inverse maps are given in terms of left and right division by

原群 ''Q''是拟群当且仅当这两个变换是双射变换，而且它们的逆变换给出了右除和左除变换

Since a ring satisfies the related comparability if and only if every regular element is related unit-regular, In Section 2. 3, we first give some equivalent conditions for an arbitrary ring to satisfy the related comparability.

由于环R满足相对可比性当且仅当R的每个正则元是相对幺正则的，§2.2节给出了一般环中给定的正则元是相对幺正则的一些特征刻画，证明了文献[22]（1997）的主要结果在任意环中仍然成立。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。