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subgroup    音标拼音: [s'ʌbgr,up]
n. 小群,隶属的小组织,子群

小群,隶属的小组织,子群

subgroup
子群

subgroup
n 1: a distinct and often subordinate group within a group
2: (mathematics) a subset (that is not empty) of a mathematical
group

Subgroup \Sub"group`\, n. (Biol.)
A subdivision of a group, as of animals. --Darwin.
[1913 Webster]


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  • Subgroups of $\\mathbb{Z}$ - Mathematics Stack Exchange
    "H of G is called a subgroup of G if H also forms a group under the operation ∗"!!AND!!! to be a SUB
  • Difference between conjugacy classes and subgroups?
    As others said subgroup has all the properties of Group But conjugacy classes are just the set, but created with conjugacy and are equivalence relation Intuitively conjugacy is, looking the same thing with different perspective For ex take ${D_6}$, a hexagon and say r=clockwise rotation and f=horizontal reflection
  • How do I find all all the subgroups of a group?
    I understand the requirements of a subgroup (associativity, identity etc ) but I don't actually know how to find the subgroups I think it has something to do with "getting back to the identity", but I may be wrong? I know that the identity is a subgroup and the whole group is a subgroup That's all Any help would be appreciated!
  • group theory - Subgroups of $D_3$ - Mathematics Stack Exchange
    There are three elements of order $2$, namely $(12)$, $(13)$, and $(23)$, and each of these is in a distinct subgroup of order $2$, so there are three subgroups of order $2$ Finally, of course, there are the trivial subgroup and the full group We have covered all possible subgroup orders, so we're done
  • group theory - Subgroup criterion. - Mathematics Stack Exchange
    If H is a subset of G, prove that H is also a subgroup 4 Subset of $\mathbb{R}$ is closed under multiplication when it contains $1$ and is closed under subtraction and inverses
  • How to find all subgroups of - Mathematics Stack Exchange
    $\begingroup$ The subgroup generated by 1 and 1 2 is generated by 1 2 alone There are two cases: there is a smallest positive element in this subgroup (which you must show generates the group), or there is none In the second case, look at the set of denomiators inside the integers and try to find its structure $\endgroup$ –
  • Understanding how to prove when a subset is a subgroup
    Lemma 3 4 Let $(G ,*)$ be a group A nonempty subset $H$ of $G$ is a subgroup of $(G,*)$, iff, for every $a, b\in H$, $a*b^{-1}\in H$
  • determining number of subgroups - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • Subgroups of a direct product - Mathematics Stack Exchange
    Until recently, I believed that a subgroup of a direct product was the direct product of subgroups Obviously, there exists a trivial counterexample to this statement I have a question regarding
  • Find the subgroups of A4 - Mathematics Stack Exchange
    $\begingroup$ A subgroup of order 3 is isomorphic to $\Bbb Z_3$, so it is generated by an element of order 3 To identify the subgroups of order 3 it suffices to identify the elements of order 3 $\endgroup$ –





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