3.3. The greatest common divisor and the least common multiple 12 3.4. Parabolic divisors 14 3.5. Divisibility: further properties 14 4. Normal forms arising from HNN extensions 16 4.1. HNN -normal form 16 5. Conjugacy problem 18 5.1. Conjugacy Criterion for HNN -extensions 18 5.2. Block decomposition 22 5.3. Conjugacy with respect to a subgroup 23 5.4. An algorithm for solving the Conjugacy Pr...

The main result of the paper is a new formula for the number of conjugacy classes of subgroups of a given index in a finitely generated group. As application of this result a simple proof of the formula for the number of non-equivalent coverings over surface (orientable or not, bordered or not) is given. Another application is a formula for the number of non-isomorphic unrooted maps on an orien...

When examining the structure of a finite group G, a typical question is the determination of the conjugacy classes of subgroups. For this problem a well-known algorithm – the cyclic extension method (Neubüser 1960, Mnich 1992) – has been in use for over 30 years. For practical purposes this algorithm is limited to groups of size a few thousand. If the subgroup lattice is very thin the possible ...

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group Mσ of a compact closed surface X of genus σ is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumera-tion of finite abelian subgroups.

a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...

‎the purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the fischer matrices and the ordinary‎ ‎character table of the split extension $overline{g}=‎ ‎3^{7}{:}sp(6,2)$ by means of clifford-fischer theory‎. ‎we firstly‎‎determine the conjugacy classes of $overline{g}$ using the coset‎ ‎analysis method‎. ‎the determination of the inertia factor groups of‎ ‎...