Skip to main content
MathOverflow

Return to Answer

deleted 1 character in body
Source Link
Yakov
Yakov
  • 103
  • 3

Problem 1. Classify the nonabelian p-groups G such that Z(G) is contained in the union of minimal nonabelian subgroups of G.

Problem 2 (old problem). Classify the p-groups covered by their minimal nonabelian subgroups.

A set of subgroups of a group G cover G is the union of these subgroups coincides with G. For example, the dihedral group D of order 2^4 is not covered by its minimal nonabelian duchgroupssubgroups since exp(D)=2^3 and exponents of all its minimal nonabelian subgroups equal 2^2.

Yakov

Problem 1. Classify the nonabelian p-groups G such that Z(G) is contained in the union of minimal nonabelian subgroups of G.

Problem 2 (old problem). Classify the p-groups covered by their minimal nonabelian subgroups.

A set of subgroups of a group G cover G is the union of these subgroups coincides with G. For example, the dihedral group D of order 2^4 is not covered by its minimal nonabelian duchgroups since exp(D)=2^3 and exponents of all its minimal nonabelian subgroups equal 2^2.

Yakov

Problem 1. Classify the nonabelian p-groups G such that Z(G) is contained in the union of minimal nonabelian subgroups of G.

Problem 2 (old problem). Classify the p-groups covered by their minimal nonabelian subgroups.

A set of subgroups of a group G cover G is the union of these subgroups coincides with G. For example, the dihedral group D of order 2^4 is not covered by its minimal nonabelian subgroups since exp(D)=2^3 and exponents of all its minimal nonabelian subgroups equal 2^2.

Yakov

Source Link
Yakov
Yakov
  • 103
  • 3

Problem 1. Classify the nonabelian p-groups G such that Z(G) is contained in the union of minimal nonabelian subgroups of G.

Problem 2 (old problem). Classify the p-groups covered by their minimal nonabelian subgroups.

A set of subgroups of a group G cover G is the union of these subgroups coincides with G. For example, the dihedral group D of order 2^4 is not covered by its minimal nonabelian duchgroups since exp(D)=2^3 and exponents of all its minimal nonabelian subgroups equal 2^2.

Yakov