Add to ORKGAbstract. It is a known fact that the subgroup 2(G) generated by all elements of order at most 4 in a nite 2-group G has a strong in uence on the structure of the whole group. Here we determine nite 2-groups G with jGj> 16 and j 2(G)j = 16. The resulting groups are only in one case metacyclic and we get in addition eight innite classes of non-metacyclic 2-groups and one exceptional group of order 25. All non-metacyclic 2-groups will be given in terms of generators and relations. In addition we determine completely nite 2-groups G which possess exactly one abelian subgroup of type (4; 2). 1
A group G is metacyclic if it contains a cyclic normal subgroup K such that G/K is also cyclic. Fini...
In this paper, G denotes a metacyclic 2-group of order at most 32 and ? denotes a simple undirected ...
AbstractTwo theorems are proved, the first of them showing that a modular quaternion-free finite 2-g...
It is a known fact that the subgroup (G) generated by all elements of order at most 4 in a finite 2-...
Abstract. In this paper we classify nite non-metacyclic 2-groups G such that 2(G) (the subgroup gene...
In this paper we classify finite non-metacyclic 2-groups G such that Ω2*(G) (the subgroup generated ...
AbstractWe classify here the title groups and note that such groups must be of exponent >4 if both D...
summary:We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank ...
Abstract. We determine completely the structure of finite 2-groups which possess exactly six cyclic ...
Abstract. We shall determine the title groups G up to isomorphism. This solves the problem Nr.861 fo...
Abstract. We describe rst the structure of nite minimal nonmod-ular 2-groups G. We show that in case...
We determine completely the structure of finite 2-groups which possess exactly six cyclic subgroups ...
Let P be a group theoretical property. There are many results in literature concerning groups in whi...
AbstractIn Theorem 2.3 we determine finite 2-groups all of whose minimal nonabelian subgroups are of...
A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this pa...
A group G is metacyclic if it contains a cyclic normal subgroup K such that G/K is also cyclic. Fini...
In this paper, G denotes a metacyclic 2-group of order at most 32 and ? denotes a simple undirected ...
AbstractTwo theorems are proved, the first of them showing that a modular quaternion-free finite 2-g...
It is a known fact that the subgroup (G) generated by all elements of order at most 4 in a finite 2-...
Abstract. In this paper we classify nite non-metacyclic 2-groups G such that 2(G) (the subgroup gene...
In this paper we classify finite non-metacyclic 2-groups G such that Ω2*(G) (the subgroup generated ...
AbstractWe classify here the title groups and note that such groups must be of exponent >4 if both D...
summary:We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank ...
Abstract. We determine completely the structure of finite 2-groups which possess exactly six cyclic ...
Abstract. We shall determine the title groups G up to isomorphism. This solves the problem Nr.861 fo...
Abstract. We describe rst the structure of nite minimal nonmod-ular 2-groups G. We show that in case...
We determine completely the structure of finite 2-groups which possess exactly six cyclic subgroups ...
Let P be a group theoretical property. There are many results in literature concerning groups in whi...
AbstractIn Theorem 2.3 we determine finite 2-groups all of whose minimal nonabelian subgroups are of...
A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this pa...
A group G is metacyclic if it contains a cyclic normal subgroup K such that G/K is also cyclic. Fini...
In this paper, G denotes a metacyclic 2-group of order at most 32 and ? denotes a simple undirected ...
AbstractTwo theorems are proved, the first of them showing that a modular quaternion-free finite 2-g...