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1.
Let G be a finite group and
e(G) the set of element orders of G. Denote by h(
e(G)) the number of isomorphism classes of finite groups H satisfying
e(H) =
e(G). We prove that if G has at least three prime graph components, then h(
e
(G)){1, }. 相似文献
2.
3.
4.
IfG is a finite group in which every element ofp′-order centralizes aq-Sylow subgroup ofG, wherep andq are distinct primes, it is shown thatO
q′
(G) is solvable,l
q
(G)≤1 andl
p
(O
q′
(G)) ≤2. Further, the structure ofG is determined to some extent.
Work partially supported by MURST research program “Teoria dei gruppi ed applicazioni”. 相似文献
5.
We focus our attention on the linear groups L n (2) and obtain some general properties of these groups. We will show then that the linear groups L p (2), where 2 is a primitive root mod p (p odd prime), are recognizable by spectrum. For example, the linear groups L 3(2), L 5(2), L 11(2), L 13(2), L 19(2), L 29(2), L 37(2), L 53(2), etc. are recognizable by spectrum. 相似文献
6.
We classify the C55-groups, i.e., finite groups in which the centralizer of every 5-element is a 5-group. 相似文献
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