 About 103,000 results  books.google.com We may also consider the following subsets of G: • the set Tor(G) of its elements
of finite order, the torsion of G, • the set G[n] of its elements of order dividing n, for
any n < u>, • the set Gp of its pelements, the ppart of G, for any prime p, and ... 

 books.google.com As Fp is the union ∪i≥1Fpi of finite fields, any g ∈ G lies in GLn(Fq) for some
power q of p, so has finite order. Then gs is ... By the uniqueness of the p and p
parts of elements of finite groups, the claim follows. See [32, Thm. 15.3] for a
proof ... 

 books.google.com 7}) = r, and part (i) of the lemma is proved. (ii) The proof is analogous to the last
part of (i) taking S, in place of T,. Let x be an element of a group G and let p be a
prime. Then x is called a pelement (or “psingular”) if its order is a power of p, ... 

 books.google.com D The treatment of divisible groups containing nontrivial elements of finite order
needs some more preparation. ... Thus the union Ap := UneN ker E?A ls a
subgroup, called the ppart of A, or a primary subgroup of A. 4.19 Example. Using
the ... 

 books.google.com Linear algebraic groups, or Fgroups, are defined as affine Fvarieties with a
group structure such that multiplication and ... any element of G is of finite order
and its Jordan decomposition coincides with its decomposition into ppart and p' 
part ... 

 books.google.com The theory of abstract finite simple groups is built on the intimate relations
between general group theory, ordinary ... Brauer began his lecture at the
International Congress in 1954 as follows: “The theory of groups of finite order
has been ... It yields an explicit character formula χ(g) for all irreducible
characters χ of G belonging to a pblock B of G with defect group D and all
elements g of G whose ppart gp ... 

 books.google.com This implies that R has a basis as a Zmodule consisting of the elements 1, w, a>
2, a>*~i, where n = deg /(Z). We shall ... Finally two elements x, y of G will be said
to be pconjugate if their /)'parts are conjugate in the ordinary sense. Since the ... 

 books.google.com The groups H and Q are called complementary groups as regards G, and the
product of their orders is equal to the order ... cosets it results directly that every
subgroup of index p under any group includes a p'th, p' 2 p, part of the elements
of ... 

 books.google.com We deduce that the integers ]_[K€c,(G0) CG(a:K) and det(C) have the same p
part, as desired. I We now discuss ... If G is a group, a p'section of G is the set of
all elements of G whose p' part is conjugate to some fixed 9: G G0. This is ...
important p'section of G is the set G1, of the elements of G which have ppower
order. 

 books.google.com Many authors print the conjugacy classes in various kinds of order that reflects
their makeup. For instance an element of order p might immediately be followed
by the elements of orders 2p, 3p, . . . that have it for their ppart. This helps the ... 

 