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We study groups with an H-Frobenius element and the nilpotent kernels of the corresponding Frobenius subgroups. We prove the two theorems that solve Question 10.61 of The Kourovka Notebook in this case.

We study the structure of an infinite group with automorphism of order 2p, where p is an odd prime leaving only the identity element fixed.

We prove Jordan’s Theorem for infinite sharply 2-transitive groups satisfying the finiteness (a, b)-condition, with |a| · |b| even.