Browsing by Subject "Fixed point free separability"

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    A Fitting height lemma and its applications
    (Springer Nature Switzerland AG, 2021-05-02) Kızmaz, Muhammet Yasir
    Let A be a group acting on a solvable group G and let N be an A-invariant normal subgroup of G such that [G, A] N. We prove the inequality h([G, A]) ≤ h([G, A]N/N) + h([N,A]) where h(G) denotes the Fitting height of G. As an application of this result, we obtain several Fitting height inequalities. A new concept “fixed point free separability” and a new characteristic subgroup Y (G) is defined and used in order to prove some further results about the Fitting height of a group. In the last section, a new characterization of solvable groups is given: a group G is solvable if and only if it is fixed point free separable