Equation 677 Database

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Magma 21f5f8252705…

magma 21f5f8252705
Size
595
Isomorphism class hash
21f5f8252705168d8be5e9e3103a40f12c5c035917889521eb46feaee21a38fd
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
2026-10-08 01:54:04
Display reorder
48,47,49,50,51,46,90,89,85,86,87,88,8,7,9,10,11,12,458,456,457,459,460,461,405,407,406,404,402,403,519,530,569,554,566,237,239,173,235,236,238,170,144,140,141,142,143,39,38,34,35,36,37,63,62,61,193,194,155,211,210,212,163,132,133,136,135,137,138,139,226,169,228,229,230,227,168,186,185,187,154,188,189,328,327,326,324,325,323,498,497,496,493,495,494,395,394,393,392,390,391,486,488,487,489,490,491,432,433,434,437,435,436,311,310,309,306,307,308,440,441,439,443,438,442,263,262,261,259,258,260,551,550,524,518,536,537,517,527,573,584,588,590,589,567,553,591,28,30,31,32,33,29,105,104,106,107,102,103,112,111,113,108,109,110,121,120,122,123,124,125,2,1,3,4,5,0,56,55,52,53,54,190,205,160,206,203,204,159,222,221,167,223,224,225,305,304,303,301,302,300,288,290,289,293,291,292,367,366,365,370,368,369,428,426,427,431,429,430,509,507,506,508,504,501,361,360,359,362,363,364,421,422,420,424,425,423,492,503,500,505,499,502,541,515,525,548,549,534,526,514,582,556,565,577,578,580,587,557,91,93,94,95,96,92,84,83,79,80,81,82,23,22,24,25,26,27,75,74,76,77,78,73,118,117,119,114,115,116,146,145,147,148,149,257,250,247,251,248,249,240,256,255,246,252,253,254,449,447,448,444,445,446,313,312,314,315,389,316,386,388,387,383,384,385,379,378,377,382,380,381,321,320,322,319,317,318,283,282,284,287,285,286,451,452,450,454,455,453,281,280,279,276,277,278,531,538,529,510,516,542,528,511,560,581,594,564,592,579,559,571,131,127,128,129,130,126,6,181,182,179,152,180,176,151,175,150,177,178,196,195,156,72,70,71,98,97,99,100,201,202,172,232,233,234,171,231,158,199,200,197,198,157,242,241,244,174,243,245,413,412,411,409,410,408,483,485,484,482,481,480,355,354,353,358,356,357,465,467,466,463,462,464,299,298,297,294,295,296,371,373,372,375,376,374,265,264,266,269,267,268,331,330,329,332,333,334,544,547,523,521,512,522,513,520,558,572,563,562,570,561,593,583,41,43,44,45,40,42,134,219,220,166,217,218,213,165,214,215,164,216,184,183,153,20,21,19,57,60,58,59,191,192,208,207,161,209,162,101,67,66,68,69,64,65,17,16,18,13,14,15,350,352,351,349,347,348,396,398,397,401,399,400,341,343,342,344,345,346,340,339,338,337,335,336,473,472,471,468,469,470,271,270,272,275,273,274,418,417,419,416,414,415,479,478,477,474,475,476,540,539,532,546,545,535,543,533,552,555,576,586,568,585,575,574 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 {18, 42} (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 2026-10-08 01:54:05 · history