Equation 677 Database

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Magma 6442a3163dee…

magma 6442a3163dee
Size
401
Isomorphism class hash
6442a3163dee4a1b9ecc519cfa06dec2db7fb305d0dbc719739a50ddc646cb6f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 400) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 08:39:00
Display reorder
400,176,248,177,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,297,291,292,293,294,295,296,298,299,300,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,155,156,157,158,159,160,178,179,180,181,182,183,184,185,186,301,302,303,304,305,306,307,337,342,348,355,356,390,389,391,384,385,386,387,388,338,345,343,271,272,273,274,268,269,270,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,227,228,229,325,326,327,328,329,330,331,332,333,334,232,234,236,238,240,242,244,223,224,225,226,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,246,358,351,376,375,377,380,378,379,373,374,103,247,104,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,114,115,116,117,45,57,47,48,49,50,51,52,53,58,54,55,56,253,254,251,250,267,265,287,290,289,288,46,105,106,107,108,109,110,111,112,113,282,283,284,285,286,252,266,336,341,347,353,354,360,361,362,363,364,365,366,367,339,349,344,318,319,320,321,322,323,324,217,218,219,220,221,222,206,207,208,209,210,211,212,213,214,215,216,190,191,192,193,194,195,196,4,3,2,1,0,230,231,233,235,237,239,241,243,187,188,189,308,311,312,313,314,315,316,317,309,310,197,198,199,200,201,202,203,204,205,249,359,357,395,394,396,397,398,399,392,393,6,245,5,10,11,12,13,14,15,16,17,18,19,20,21,22,23,7,8,9,255,256,257,258,259,260,261,262,263,264,34,35,36,37,38,39,40,41,42,43,44,24,25,26,27,28,29,30,31,32,33,94,95,96,97,98,99,100,101,102,275,276,277,278,279,280,281,335,340,346,350,352,381,383,382,368,369,370,371,372 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 401 = 1 + 5*80, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#27b44223aba3901db5370d269eb5ae773e533f1b11b5ba8e68f30c1a3464cf50, M = {80} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 80): MacNeish's product over GF(16) x GF(5); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 1.

last edited by qawbecrdtey at 2026-10-02 08:39:07 · history