Characterizations of hypercyclically embedded subgroups of finite groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 195-206.

A normal subgroup H of a finite group G is said to be hypercyclically embedded in G if every chief factor of G below H is cyclic. Our main goal here is to give new characterizations of hypercyclically embedded subgroups. In particular, we prove that a normal subgroup E of a finite group G is hypercyclically embedded in G if and only if for every different primes p and q and every p-element a(G ' F * (E))E ' , p ' -element bG and q-element cG ' we have [a,b p-1 ]=1=[a q-1 ,c]. Some known results are generalized. \end{abstract}

DOI : 10.4171/RSMUP/135-11
Classification : 20
Mots clés : Finite group, supersoluble group, hypercyclically embedded subgroup, Sylow subgroup, generalized Fitting subgroup
Yi, Xiaolan 1

1 Zhejiang University of Science and Technology, HANGZHOU, CHINA
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     author = {Yi, Xiaolan},
     title = {Characterizations of hypercyclically embedded subgroups of finite groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {195--206},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {135},
     year = {2016},
     doi = {10.4171/RSMUP/135-11},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/135-11/}
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Yi, Xiaolan. Characterizations of hypercyclically embedded subgroups of finite groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 195-206. doi : 10.4171/RSMUP/135-11. http://www.numdam.org/articles/10.4171/RSMUP/135-11/

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