Subgroup Lattices of Groups (De Gruyter Expositions in Mathematics)

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When G is a cyclic group or an elementary abelian p-group this problem can completely or partially be solved. These situations are treated in Sections 2 and 3, respectively.

Most of our notation is standard and will usually not be repeated here. For lattice theory and group theory concepts we refer the reader to [2,13].

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Consequently, Eq. Theorem 1. Thus the statement P 1 is obviously true. We shall study the properties of this sequence using rules that hold in the ring of formal series. Thus, multiplying Eq. Corollary 4.

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Corollary 5. A spe- cial class of abelian p-groups is constituted by elementary abelian p-groups.


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L Z By analyzing Fig. First, we need more information about the subgroup lattice of Zkp. The number of all subgroups of an arbitrary order in Zkp is given by [15] see Corollary 2 of Proposition 2, Section 2. Proposition 7. We begin by making an auxiliary construction.

Subgroup Lattices of Groups (De Gruyter Expositions in Mathematics)

Moreover, by using a computer algebra program, we can easily obtain all the xr,s. Therefore, we have proved the next proposition. Proposition 8.


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Now, we are able to establish the main result of this section. Theorem 9.

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Corollary This may constitute the subject of some future studies. Acknowledgments The author is grateful to the reviewers for their remarks which improve the previous version of the paper. References [1] P. Flajolet, R. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and Systems 73 —; T.

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Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and Systems 79 — [4] D. Kumar, Fuzzy Algebra, vol. I, University of Delhi, Publication Division, Mordeson, N.

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Subgroup lattices of groups

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