Geodesic
On Finite Groups with Some Conditions on Subsets
Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let be a positive integer. We denote by the class of groups such that, for every subset of of cardinality , there exist a positive integer , and a subset , with and a function , with and non-zero integers such that , where , , and whenever , for some subgroup of . If the integer is fixed for every subset we obtain the class . If one always has , , and , , one obtains the class . In this paper, we prove that (1) A finite semi-simple group has the property , for some , if and only if or , (2) A finite non-nilpotent group has the property , for some , if and only if , where is the hypercenter of , (3) A finite semi-simple group has the property , for some , if and only if , where and denote the alternating and symmetric groups of degree n respectively.
Classification : 20F99, 20F45. 
@article{BMMS_2009_32_1_a6,
     author = {Bijan Taeri},
     title = {On {Finite} {Groups} with {Some} {Conditions} on {Subsets}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2009},
     volume = {32},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2009_32_1_a6/}
}
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%J Bulletin of the Malaysian Mathematical Society
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Bijan Taeri. On Finite Groups with Some Conditions on Subsets. Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2009_32_1_a6/