Equation 677 Database

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Magma 42df9fcd59f5…

magma 42df9fcd59f5
Size
399
Isomorphism class hash
42df9fcd59f5078d986bd5663d240fae28b66a997385866c6354d69e9b1d9f6f
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 19:03:48
Display reorder
63,64,65,66,67,68,69,70,71,55,56,57,58,59,60,61,62,54,398,264,236,282,265,237,283,266,238,284,267,239,285,268,240,286,269,241,287,261,242,279,262,234,280,263,235,281,256,245,274,257,246,275,258,247,276,259,248,277,260,249,278,252,250,270,253,251,271,254,243,272,255,244,273,304,297,298,299,300,301,302,303,296,288,289,290,291,292,293,294,295,305,397,383,382,396,191,163,131,192,164,132,193,165,133,194,166,134,195,167,126,196,168,127,197,169,128,189,170,129,190,162,130,183,172,140,184,173,141,185,174,142,186,175,143,187,176,135,188,177,136,180,178,137,181,179,138,182,171,139,144,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,145,384,394,395,385,88,110,200,89,111,201,81,112,202,82,113,203,83,114,204,84,115,205,85,116,206,86,108,198,87,109,199,80,119,209,72,120,210,73,121,211,74,122,212,75,123,213,76,124,214,77,125,215,78,117,207,79,118,208,98,91,92,93,94,95,96,97,107,99,100,101,102,103,104,105,106,90,387,390,391,386,324,322,342,325,323,343,326,315,344,327,316,345,328,317,346,329,318,347,330,319,348,331,320,349,332,321,350,333,314,351,334,306,352,335,307,353,336,308,354,337,309,355,338,310,356,339,311,357,340,312,358,341,313,359,374,373,375,376,361,362,360,372,365,366,367,368,369,370,371,363,364,377,393,389,388,392,216,0,31,217,2,32,218,3,33,219,4,34,220,5,35,221,6,27,222,7,28,223,8,29,224,1,30,225,10,23,226,11,24,227,12,25,228,13,26,229,14,18,230,15,19,231,16,20,232,17,21,233,9,22,53,46,47,48,49,50,51,52,36,37,38,39,40,41,42,43,44,45,380,378,381,379 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#86b36e5e6676aa6f0bebace581d87a3f890996e461e9718d4d5bc414dada2c24, 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 19:03:49 · history