A class of Abelian groups closed under direct limits and subgroups formation

Generalized Covering Groups and Direct Limits

Finite $p$-groups and centralizers of non-cyclic abelian subgroups

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.

Limits of Abelian Subgroups of Finite p-groups

Abelian subgroups play a key role in the theory and applications of finite p-groups. Our purpose is to establish some very general results motivated by special results that have been of use. In particular, it is known [KJ] that if a finite p-group, for odd p, has an elementary abelian subgroup of order p, n ≤ 5, then it has a normal elementary abelian subgroup of the same order. Our first main ...

The number of Fuzzy subgroups of some non-abelian groups

In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are givenfor dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.

COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS

In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...