Assertion: abelian group's subgroup | /r/HasProperty | abelian
Facets:
value: for a finite field
type: OTHER
Source sentences:
text: In my mind it makes sense that I cannot lose commutativity therefore my subgroup must be Abelian too.
text: A group G satisfies the minimality condition for subgroups (Abelian subgroups), if in G every decreasing chain of subgroups (Abelian subgroups) H 1 >
text: Any two maximal subgroups of intersect trivially every proper subgroup of is abelian Step (1)
text: In particular, for a finite field F with odd characteristic, the 2-Sylow subgroup of SL 2 (F) is non-abelian and has only one subgroup of order 2, so this 2-Sylow subgroup must be a generalized quaternion group, (Gorenstein 1980, p. 42).
text: the subgroup R = {id, r 1 , r 2 , r 3 }, as well as the corresponding quotient are abelian, whereas D 4 is not abelian.
text: Further facts about every proper subgroup being abelian
text: Given: A finite non-abelian group such that every proper subgroup of is abelian.
text: The derived subgroup cannot be trivial since is non-abelian, hence the derived subgroup must be .
text: A discrete normal subgroup of a connected group G necessarily lies in the center of G and is therefore abelian.
text: A group G satisfies the minimality condition for subgroups (Abelian subgroups), if in G every decreasing chain of subgroups (Abelian subgroups) H 1 >