Equation 677 Database

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Magma cfd97f69dfb2…

magma cfd97f69dfb2
Size
595
Isomorphism class hash
cfd97f69dfb22898237c229d364cd8458e6fad68f0ab38dcf9912cec1a6589b8
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:14:04
Display reorder
76,78,79,80,81,77,112,111,113,114,115,116,39,38,40,41,36,37,287,288,430,290,291,289,332,331,333,330,328,329,512,538,570,581,571,200,199,158,201,202,198,153,30,31,32,28,29,122,121,123,124,125,120,118,117,119,226,227,168,209,208,210,161,89,88,73,72,74,75,71,203,163,214,215,216,213,164,182,181,183,152,184,185,302,301,303,298,299,300,509,508,507,505,506,504,341,340,342,344,345,343,317,316,318,320,321,319,385,384,383,386,387,388,454,453,452,450,449,451,266,268,267,264,265,263,491,490,489,486,488,487,550,551,519,510,529,528,520,526,562,573,567,566,582,563,586,565,91,90,92,93,94,95,18,17,19,20,21,16,62,61,63,64,59,60,104,103,99,100,101,102,1,0,2,3,4,5,139,138,140,141,142,232,229,170,230,231,228,169,223,222,167,224,225,221,503,502,501,499,500,498,394,393,392,390,391,389,262,261,369,258,260,259,492,494,493,495,496,497,460,459,461,458,457,456,415,414,413,416,417,429,323,322,324,327,325,326,425,424,426,427,428,431,527,531,514,548,549,542,543,532,579,560,590,574,585,584,561,558,68,67,69,70,65,66,25,24,26,27,22,23,11,10,12,13,14,15,57,56,58,53,54,55,106,105,107,108,109,110,146,145,147,148,149,257,253,247,256,255,254,245,252,251,246,249,248,250,372,371,373,374,375,376,379,378,377,381,382,380,362,361,368,359,360,358,309,308,307,306,304,305,440,439,438,441,442,443,446,448,447,445,455,444,348,347,346,349,350,351,365,364,363,367,370,366,534,521,535,513,537,522,536,515,559,580,594,577,593,589,578,557,130,129,131,126,127,128,144,242,243,244,174,241,240,173,237,172,238,239,212,211,162,96,97,98,7,9,8,6,175,176,151,179,180,177,150,178,166,219,220,217,218,165,188,192,189,155,190,191,278,280,279,277,275,276,483,485,484,482,480,481,437,436,435,434,432,433,409,408,407,412,410,411,418,420,419,422,423,421,353,352,354,357,355,356,398,400,399,396,397,395,473,472,471,469,470,468,544,545,523,518,539,517,516,533,576,553,554,587,583,556,592,552,135,134,136,137,132,133,143,233,234,171,235,236,205,159,206,204,160,207,186,187,154,33,34,35,49,48,50,51,193,194,195,197,156,196,157,52,47,46,42,43,44,45,86,85,87,82,83,84,479,478,477,475,476,474,310,312,311,315,313,314,273,272,274,270,271,269,466,465,467,462,464,463,334,336,335,338,339,337,406,405,404,401,402,403,286,285,284,281,282,283,297,296,295,293,294,292,541,540,511,546,547,524,530,525,555,564,575,588,569,572,568,591 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#967d317cf04778fc566aed88226f2ec73cf112a27da243deb50eb6f078cd5ea3, M = the submagma generated by {0, 54} (35 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, 112): MacNeish's product over GF(16) x GF(7); 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: 85.

last edited by qawbecrdtey at 2026-10-06 19:14:05 · history