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nontrivial subgroup

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  • Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… …   Wikipedia

  • Subgroup — This article is about the mathematical concept For the galaxy related concept, see Galaxy subgroup. Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum …   Wikipedia

  • No small subgroup — In mathematics, especially in topology, a topological group G is said to have no small subgroup if there exists a neighborhood U of the identity that contains no nontrivial subgroup of G. An abbreviation NSS is sometimes used. A basic example of… …   Wikipedia

  • Fitting subgroup — In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G , named after Hans Fitting, is the unique largest normal nilpotent subgroup of G . Intuitively, it represents the smallest… …   Wikipedia

  • Frattini subgroup — Hasse diagram of the lattice of subgroups of the dihedral group Dih4 In the 3 element layer are the maximal subgroups; their intersection (the F. s.) is the central element in the 5 element layer. So Dih4 has only one non generating element… …   Wikipedia

  • Free abelian group — In abstract algebra, a free abelian group is an abelian group that has a basis in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients …   Wikipedia

  • Solvable group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

  • Complemented group — In mathematics, in the realm of group theory, the term complemented group is used in two distinct, but similar ways. In (Hall 1937), a complemented group is one in which every subgroup has a group theoretic complement. Such groups are called… …   Wikipedia

  • Stallings theorem about ends of groups — In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or… …   Wikipedia

  • Ping-pong lemma — In mathematics, the ping pong lemma, or table tennis lemma, is any of several mathematical statements which ensure that several elements in a group acting on a set freely generate a free subgroup of that group.HistoryThe ping pong argument goes… …   Wikipedia

  • N-group (finite group theory) — In mathematical finite group theory, an N group is a group all of whose local subgroups (that is, the normalizers of nontrivial p subgroups) are solvable groups. The non solvable ones were classified by Thompson during his work on finding all the …   Wikipedia

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