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FC-gruppi e proiettività

Carmela Musella (2001)

Bollettino dell'Unione Matematica Italiana

Some lattice properties of FC-groups and generalized FC-groups are considered in this paper.

Finite groups whose all proper subgroups are 𝒞 -groups

Pengfei Guo, Jianjun Liu (2018)

Czechoslovak Mathematical Journal

A group G is said to be a 𝒞 -group if for every divisor d of the order of G , there exists a subgroup H of G of order d such that H is normal or abnormal in G . We give a complete classification of those groups which are not 𝒞 -groups but all of whose proper subgroups are 𝒞 -groups.

Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements

Changguo Shao, Qinhui Jiang (2014)

Czechoslovak Mathematical Journal

Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups G whose set of numbers of subgroups of possible orders n ( G ) has exactly two elements. We show that if G is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then G has a normal Sylow subgroup of prime order and G is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with...

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