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Generation of finite groups by nilpotent subgroups

E. Damian (2003)

Bollettino dell'Unione Matematica Italiana

We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by n nilpotent subgroups and such that every proper quotient can be generated by n nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.

Groups where each element is conjugate to its certain power

Pál Hegedűs (2013)

Open Mathematics

This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power g n. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.

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