The normalizer property for integral group rings of finite solvable T-groups

Abstract

Abstract. A group is said to be a T-group if all its subnormal subgroups are normal. Let G be a finite solvable T-group. It is shown that the normalizer property holds for G. As a direct consequence of our result, we obtain that the normalizer property holds for finite groups all of whose Sylow subgroups are cyclic.

Coleman Automorphisms of Permutational Wreath Products

“…Hertweck [2] constructed a group G of order 2 25 · 97 2 for which the normalizer property fails. For positive results on the normalizer problem, the reader may refer to [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. According to the Coleman's result ([7, Coleman Lemma]), the normalizer property holds for G provided that Out Col G = 1.…”

Coleman Automorphisms of Standard Wreath Products of Nilpotent Groups by Groups With Prescribed Sylow 2-Subgroups

“…Nevertheless, it is still interesting to determine for which group the normalizer property holds. For more recent positive results on this topic, refer to [2,[4][5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21].…”

Coleman automorphisms of generalized dihedral groups

“…Thus it is no surprise that Coleman automorphisms of G occur naturally in the study of the normalizer problem. Related work in this direction can be found in [3][4][5][6][7][8][9][10][11][12]. However, we do not intend to go into details for this.…”