A group G is core-2 if and only if |H/H_G| is at most 2 for every subgroup H of G. We prove that every core-2 nilpotent 2-group of class 2 has an abelian subgroup of index at most 4. This bound is the best possible. As a consequence, every 2-group satisfying the property core-2 has an abelian subgroup of index at most 16
Abstract. It is a known fact that the subgroup 2(G) generated by all elements of order at most 4 in ...
A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subg...
If H is a subgroup of the group G then we denote by H_G the normal core of H in G i.e. the intersect...
A group G is core-2 if and only if |H/H_G| is at most 2 for every subgroup H of G. We prove that eve...
AbstractA group G is core-2 if and only if |H/HG|≤2 for every H≤G. We prove that every core-2 nilpot...
For n a positive integer, a group G is called core-n if H/H_G has order at most n for any subgroup H...
AbstractForna positive integer, a groupGis calledcore-nifH/HGhas order at mostnfor every subgroupHof...
For n a positive integer, a group G is called core-n if H=HG has order at most n for every subgroup ...
We characterise groups in which every abelian subgroup has finite index in its characteristic closur...
Forna positive integer, a groupGis calledcore-nifH/H Ghas order at mostnfor every subgroupHofG(where...
AbstractIn this paper, we study the finite 2-group G such that |〈a〉G:〈a〉|⩽22 for every a∈G. We prove...
Abstract. It is a known fact that the subgroup 2(G) generated by all elements of order at most 4 in ...
A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subg...
If H is a subgroup of the group G then we denote by H_G the normal core of H in G i.e. the intersect...
A group G is core-2 if and only if |H/H_G| is at most 2 for every subgroup H of G. We prove that eve...
AbstractA group G is core-2 if and only if |H/HG|≤2 for every H≤G. We prove that every core-2 nilpot...
For n a positive integer, a group G is called core-n if H/H_G has order at most n for any subgroup H...
AbstractForna positive integer, a groupGis calledcore-nifH/HGhas order at mostnfor every subgroupHof...
For n a positive integer, a group G is called core-n if H=HG has order at most n for every subgroup ...
We characterise groups in which every abelian subgroup has finite index in its characteristic closur...
Forna positive integer, a groupGis calledcore-nifH/H Ghas order at mostnfor every subgroupHofG(where...
AbstractIn this paper, we study the finite 2-group G such that |〈a〉G:〈a〉|⩽22 for every a∈G. We prove...
Abstract. It is a known fact that the subgroup 2(G) generated by all elements of order at most 4 in ...
A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subg...
If H is a subgroup of the group G then we denote by H_G the normal core of H in G i.e. the intersect...
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