Group Theory, Volume 247Springer-Verlag, 1982 - Group theory |
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Page 126
... consider two cases according to whether the first factor group G / G , is finite or not . ) 7. Let g be a nonidentity element of a poly - cyclic group G. Show that there is a normal subgroup N ( g ) of finite index which does not ...
... consider two cases according to whether the first factor group G / G , is finite or not . ) 7. Let g be a nonidentity element of a poly - cyclic group G. Show that there is a normal subgroup N ( g ) of finite index which does not ...
Page 186
... consider the presen- tations ( XR ) of these groups , it is usually assumed that the sets X are mutually disjoint ... Consider the totality of finite sequences ( a1 , ... , a , ) of elements a , of Ga ,. Among sequences , we will ...
... consider the presen- tations ( XR ) of these groups , it is usually assumed that the sets X are mutually disjoint ... Consider the totality of finite sequences ( a1 , ... , a , ) of elements a , of Ga ,. Among sequences , we will ...
Page 310
... consider even numbers as possible candidates for the orders of nonabelian simple groups . There is another famous ... consider a group consisting of linear transformations of a vector space V over F. It is convenient to define the ...
... consider even numbers as possible candidates for the orders of nonabelian simple groups . There is another famous ... consider a group consisting of linear transformations of a vector space V over F. It is convenient to define the ...
Common terms and phrases
a₁ abelian group additive group automorphism B₁ central extension Chapter cohomology commutator composition series conjugate Corollary corresponding cosets of H Coxeter group Coxeter system cyclic group defined definition denote direct product direct sum element g element of G elements of order endomorphism Example Exercise extension H factor group factor set finite group formula free abelian group free group function G-set G₁ GL(V group G group of order H₁ H₂ Hence Hint homomorphism induces integer irreducible isomorphic K₁ lemma Let F Let G Let H mapping matrix maximal subgroup natural number normal subgroup notation p-group permutation prime number Proof prove Q-invariant representation group S,-subgroup S₁ satisfies semidirect product sequence Show simple groups SL(V solvable subgroup H subgroup of G subset subspace Suppose Sylow's Theorem transvection u₁ uniquely determined v₁ vector space w₁ w₂ Weyl group wreath product