Group elements of prime power index
نویسندگان
چکیده
منابع مشابه
Group Elements of Prime Power Index
The index [G:g] of the element g in the [finite] group G is the number of elements conjugate to g in G. The significance of elements of prime power index is best recognized once one remembers Wielandt's Theorem that elements whose order and index are powers of the same prime p are contained in a normal subgroup of order a power of p and Burnside's Theorem asserting the absence of elements of pr...
متن کاملGroup Elements of Prime Power Index
The index [G:g] of the element g in the [finite] group G is the number of elements conjugate to g in G. The significance of elements of prime power index is best recognized once one remembers Wielandt's Theorem that elements whose order and index are powers of the same prime p are contained in a normal subgroup of order a power of p and Burnside's Theorem asserting the absence of elements of pr...
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We determine all nite groups G which admit a subgroup K of index p a ; p a prime, under the assumption that G has an irreducible and faithful GF (p)-module of dimension at most a. As an application to the theory of permutation groups we determine the maximal transitive subgroups of the primitive aane permutation groups.
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متن کاملσ-sporadic prime ideals and superficial elements
Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1953
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1953-0055340-0