A Characterization Of A Class Of 2-Groups By Their Endomorphism Semigroups

On endomorphisms of groups of order 32 with maximal subgroups C4 x C2 x C2

“…Therefore, the groups G 2 − G 4 and G 8 − G 14 are determined by their endomorphism semigroups in the class of all groups. The groups G 16 and G 20 are also determined by their endomorphism semigroups in the class of all groups [4,12]. To prove Theorem 1.1, we have to prove in addition that the groups G 18 , G 36 , G 37 , and G 38 are determined by their endomorphism semigroups in the class of all groups.…”

“…The groups G 1 − G 7 are Abelian, and, therefore, are determined by their endomorphism semigroups in the class of all groups ( [7], Theorem 4.2). In [3], it was proved that the groups of order 32, presentable in the form (C 4 ×C 4 ) C 2 (C k -the cyclic group of order k), are determined by their endomorphism semigroups in the class of all groups. The groups of this type are G 3 , G 14 , G 16 , G 31 , G 34 , G 39 , G 41 .…”

On endomorphisms of groups of order 32 with maximal subgroupsC8 x C2

“…Hence the groups G 19 , G 21 , G 22 , G 29 , and G 30 are determined by their endomorphism semigroups in the class of all groups. It was proved in [4], Theorems 14.2,14.4,and 14.6, that the groups G 17 , G 20 , and G 27 are determined by their endomorphism semigroups in the class of all groups. The group G 26 is also determined by its endomorphism semigroup ( [13], Theorem 13.3).…”

“…The groups of this type are G 3 , G 14 , G 16 , G 31 , G 34 , G 39 , G 41 . In [4], it was proved that the groups of order 32 presentable in the form (C 8 ×C 2 ) C 2 are determined by their endomorphism semigroups in the class of all groups. The groups of this type are G 4 , G 17 , G 20 , G 26 , G 27 .…”

“…3) cz = c 2k 0 +1 a l , az = a j ; k 0 ∈ {0, 1}; j, l ∈ Z 8 , j ≡ 1 (mod 2). (5.4) The endomorphisms given by (5.2) and (5.3) are proper endomorphisms and the endomorphisms given by (5.4) are automorphisms.…”