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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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  • What do I need to show that a subset of a group is a subgroup?
    1) The identity from the group is the identity for the subgroup and is in the subgroup 2) The group is closed under inversion (group operation with inverse element) and that the inverse for the group is the inverse for the subgroup 3) The group is closed under the group product If I am wrong, please correct me with the proper approach
  • What is the difference between a Subgroup and a subset?
    A subgroup is a subset which is also a group of its own, in a way compatible with the original group structure But not every subset is a subgroup To be a subgroup you need to contain the neutral element, and be closed under the binary operation, and the existence of an inverse
  • 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 $a, b\in H$, $a*b^{-1}\in H$
  • Subgroup generated by a set - Mathematics Stack Exchange
    A subgroup generated by a set is defined as (from Wikipedia):More generally, if S is a subset of a group G, then , the subgroup generated by S, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S; equivalently, is the subgroup of all elements of G that can be expressed as the finite product of elements in S and
  • abstract algebra - 3 different subgroup tests. When to use each? are . . .
    $\begingroup$ I also noticed that all the 3 subgroup tests proofs involved using the one-step subgroup test I guess I will try multiple of problems and try all 3 and hopefully I would see which will fit the nature of the groups and subgroups $\endgroup$
  • 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 $\endgroup$ –
  • What is the difference between a subgroup and semigroup?
    A subgroup is a subset of a group that is itself closed under the group operation A semigroup is a set equipped with an operation that is merely associative, different from a group in that we assume the binary operation of a group is associative and invertible, i e each element has an inverse with respect to the operation
  • 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
  • Subgroups of dihedral group - Mathematics Stack Exchange
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  • 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





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