# Normalp-complements for finite groups

@article{Thompson1959NormalpcomplementsFF, title={Normalp-complements for finite groups}, author={John G. Thompson}, journal={Mathematische Zeitschrift}, year={1959}, volume={72}, pages={332-354} }

The minimal number of generators of the group Q is denoted m(s). We define d(B) = max m(s) where ‘21 ranges over all the abelian subgroups of EJ and we let J(cli) be the subgroup generated by all the abelian subgroups ‘u of (5 which satisfy d(B) = m(a). Clearly, if J(S) c R c Q, then J(B) is a characteristic subgroup of R, J(B) char Ji. Z(G) denotes the center of 8 and / 0, jr, is the order of a SD-subgroup of Q.

## 41 Citations

### Recognition of finite simple groupsL3(2m) ANDU3(2m) by their element orders

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It is proved that a finite group isomorphic to a simple non-Abelian group L3(2m) or U3(2m) is, up to isomorphism, recognizable by a set of its element orders. On the other hand, for every simple…

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We find counterexample to the question of W. Shi showing that, for every natural number r, there exist a finite group G such that are exactly r finite groups isoespectral with G. (AU) Author(s):…

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Let H be a subgroup of a group G. We say that H satisfies Π-property in G if |G/K: NG/K(HK/K ∩ L/K)| is a π(HK/K ∩ L/K)-number for any chief factor L/K of G. If there is a subnormal supplement T of H…

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The noncommuting graph ∇(G) of a non-abelian group G is defined as follows. The vertex set of ∇(G) is G\Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy…

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Based on the prime graph of a finite group, its order can be divided into a product of some co-prime positive integers. These integers are called order components of this group. If there exist…

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