Photo by papaioannou_kostas from unsplash
ABSTRACT In this paper, we define the concept of integral for an arbitrary group, and we try to answer this question: Which groups can be considered as a commutator subgroup?… Click to show full abstract
ABSTRACT In this paper, we define the concept of integral for an arbitrary group, and we try to answer this question: Which groups can be considered as a commutator subgroup? For instance, we will show that symmetric group Sn for n ≥ 3, generalized quaternion group for n ≥ 4 and Dihedral group Dn for n ≥ 3 cannot occur as commutator subgroup of any group. Moreover, we characterize all finite groups with the cyclic commutator subgroup isomorphic to or .
Keywords:
commutator subgroup;
integral groups;
group
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!