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In Theorem 3 we improve [8, Lemma 5.41] (= Lemma 1, below) omitting one of its conditions. In Lemma 1 the structure of T , a Sylow 2-subgroup of G, is described only. In contrast to that lemma, we describe in detail the structure of the whole group G and embedding of T in G. In Theorem 4 we consider a similar, but more general, situation for groups of odd order. 2000 Mathematics Subject Classification. 20C15.doi:10.3336/gm.39.2.03 fatcat:gefn5w3pwfbnhlbzmqv3oeq2qq