#### Glasnik Matematicki, Vol. 39, No.2 (2004), 213-220.

### ON A LEMMA OF THOMPSON

### Yakov Berkovich

Department of Mathematics, University of Haifa,
Haifa 31905, Israel

*e-mail:* `berkov@mathcs2.haifa.ac.il`

**Abstract.** In Theorem 3 we improve a lemma of Thompson
omitting one of its conditions. In that lemma the structure of
*T*, a Sylow 2-subgroup of *G*, is described only.
In contrast to that lemma, we describe in detail the structure of the
whole group *G* and embedding of *T* in *G*. In Theorem
4 we consider a similar, but more general, situation for groups of odd
order.

**2000 Mathematics Subject Classification.**
20C15.

**Key words and phrases.** Solvable, extraspecial, special
and metacyclic *p*-groups, Blackburn's theorem,
the stabilizer of a chain.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.39.2.03

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