Finite p-groups
Co Periodicity Isomorphisms between Forests of Finite p Groups
... of finite p -groups with arbitrary prime p in §2 and we explain the conceptual foundations of the virtual periodicity isomorphisms between the finite branches of coclass subtrees [1] ...
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Periodic Bifurcations in Descendant Trees of Finite p Groups
... pruned coclass trees whose infinitely many vertices share a common coclass r , reveal a repeating finite pattern (§7). These two crucial properties of finiteness and periodicity, which have been proved ...
34
Artin Transfer Patterns on Descendant Trees of Finite p Groups
... classifying finite p-groups by kernel-target patterns and for searching and identifying particular groups in descendant trees by looking for patterns defined by kernels and targets of Artin ...
39
The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
... of groups and related research ...the groups in the scope which has not been stated in existing ...of Groups, Algorithms and Programming ( GAP ) software, new algorithms are also ...
29
On noninner automorphisms of finite $p$-groups that fix the center elementwise
... studying p-groups is the conjecture of Berkovich that states every finite nonabelian p-group G has at least one noninner automorphism of order p (See [16, Problem ...
9
Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov
... Smith, Groups with all subgroups sub- normal or nilpotent-by-Chernikov, ...Locally finite groups with all subgroups subnormal or nilpotent-by- ...of groups G in which all subgroups are either ...
7
On the order of the schur multiplier of a pair of finite $p$-groups II
... of finite p- groups. He proved that if G is a finite p-group with a normal subgroup N of order p n and its quotient G/N of order p m , then the Schur multiplier of (G, N ) ...
8
Prime power lie algebras and finite p groups
... of finite nilpotent p-Lie rings and finite p-groups and it is this situation we are interested ...a finite nilpotent p-Lie ring U of nilpotency class less than p, ...
118
CH-groups which are finite $p$-groups
... Following [2], we call the group G a CH-group if the conjugacy class lengths of any two commuting noncentral elements of G are equal. Examples of CH-groups are the CA-groups (also known as AC- ...
15
The exterior squares of some crystallographic groups
... for finite p groups of nilpotency class two, infinite nonabelian 2-generator groups of nilpotency class two and symmetric groups of order six in [10], [11] and [12] ...
7
Finite local nearrings on metacyclic Miller-Moreno \(p\)-groups
... abelian p-groups of finite exponent. However in the case of finite non-abelian p-groups the situation is ...of finite p-groups with this property can be ...
17
Deep Transfers of p Class Tower Groups
... Hilbert p -Class Field Towers, p -Class Groups, p -Principalization, Quadratic Fields, Dihedral Fields of Degree 2 p ; Finite p -Groups, Two-Step Centralizers, ...
15
Finite groups are big as semigroups
... a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Jeˇ zek and Nation, G is a big semigroup) if and only if |G| ≥ ...any finite semigroup whose ...
10
Generation problems for finite groups
... Since P and K are both normal in H we can deduce that P ∩ K is also normal in ...then P ∩ K is normal in ...as P ∩ K is contained in the Frattini subgroup of P , both p and q ...
110
Conjugate factorizations of finite groups
... Observe that n ≤ | X | + ( | X 2 | − | X | ) + . . . + ( | X n | − | X n − 1 | ) = | X n | ≤ | G | hence | X | G | | = | X n | . Since 1 ∈ X | G | , X | G | ⊆ X 2 | G | and from | X | G | | = | X n | = | X 2 | G | | we ...
10
Finite groups as groups of automata with no cycles with exit
... X, P < S(X) and for every state q ∈ Q the permutation λ(q, ·) belongs to the group ...group P ≀ G is generated by (finite) automaton (with no cycles with exit) over an alphabet ...
17
Algorithms for polycyclic by finite groups
... The operation of the extended Schreier–Sims algorithm is based on the fol- lowing lemma, whose proof is a straightforward induction on the base length. Lemma 4.2. Let E be a polycyclic-by-finite group, H ď E and ...
23
Character expansiveness in finite groups
... a finite group usually consists of many conjugacy classes. In [8] a finite group G was called (conjugacy) expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at ...
9
On some invariants of finite groups
... All groups considered here are finite. Our notation will be standard, and similar to that in [5]. By an invariant of a group G we mean a nonnegative integer, say α(G), chosen in such a way that G ' H ...
7
On metacyclic subgroups of finite groups
... In the second part of the article, we are concerned with the influence of 2-generator subgroups on the structure of a group. The basic idea behind the results is the following: assume that a group G has 2-generator ...
5