Equation 677 Database

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Magma f8689f696cb7…

magma f8689f696cb7
Size
399
Isomorphism class hash
f8689f696cb7111aba40f45829724f9dea00dc3195e532e4ee48ac373db22b0f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 05:20:00
Display reorder
312,313,314,306,307,308,309,310,311,321,322,323,315,316,317,318,319,320,378,327,301,286,253,328,287,302,254,329,303,279,255,330,304,280,256,331,305,281,257,332,297,282,258,324,298,283,259,325,299,284,260,326,300,285,252,270,336,294,262,271,337,295,263,272,338,296,264,273,339,288,265,274,340,289,266,275,341,290,267,276,333,291,268,277,334,292,269,278,335,293,261,391,385,386,392,78,240,94,166,79,95,241,167,80,242,96,168,72,234,97,169,73,235,98,170,74,236,90,162,75,237,91,163,76,238,92,164,77,239,93,165,103,87,249,175,104,88,250,176,105,89,251,177,106,81,243,178,107,82,244,179,99,83,245,171,100,84,246,172,101,85,247,173,102,86,248,174,383,389,390,384,181,21,37,110,182,38,22,111,183,23,39,112,184,24,40,113,185,25,41,114,186,26,42,115,187,18,43,116,188,19,44,108,180,20,36,109,46,190,30,119,47,191,31,120,48,192,32,121,49,193,33,122,50,194,34,123,51,195,35,124,52,196,27,125,53,197,28,117,45,189,29,118,388,398,397,387,348,160,227,342,350,228,161,344,352,153,229,346,354,154,230,349,356,155,231,351,358,156,232,353,343,157,233,355,345,158,225,357,347,159,226,359,220,367,144,360,221,368,145,362,222,370,146,364,223,372,147,366,224,374,148,369,216,376,149,371,217,361,150,373,218,363,151,375,219,365,152,377,394,395,396,393,59,9,204,134,60,205,10,126,61,11,206,127,62,12,198,128,54,13,199,129,55,14,200,130,56,15,201,131,57,16,202,132,58,17,203,133,213,68,2,143,214,69,3,135,215,70,4,136,207,71,5,137,208,63,6,138,209,64,7,139,210,65,8,140,211,66,1,141,212,67,0,142,380,379,381,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#ab31eb598280940e4782d47fcd7efdf43287d609f4791396f912291df1a7001d, M = the submagma generated by {0} (19 elements) 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 05:20:01 · history