Equation 677 Database

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Magma 980a35662c5c…

magma 980a35662c5c
Size
595
Isomorphism class hash
980a35662c5c6c32673cb49da11c0030ccaff1cc9cbc82405fcac5211d925b56
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 03:12:30
Display reorder
277,276,278,281,279,280,272,270,271,273,274,275,507,506,508,509,504,505,498,499,500,501,502,503,481,480,482,483,484,485,556,555,588,587,594,60,61,63,64,62,59,123,122,124,121,119,120,50,52,51,47,48,49,67,66,65,70,68,69,232,231,233,230,229,228,43,42,41,44,45,46,130,129,128,127,125,126,243,245,244,240,242,241,200,199,198,201,202,203,406,405,407,402,403,404,329,328,324,325,326,327,418,417,419,414,415,416,307,306,308,309,310,311,408,413,409,410,411,412,399,398,400,401,396,397,319,318,320,321,322,323,540,546,512,527,531,520,517,538,553,579,564,584,559,574,591,569,163,164,166,167,165,162,8,10,9,6,7,5,17,19,18,20,21,22,168,170,169,171,172,173,226,225,227,224,222,223,25,24,23,26,27,28,12,11,13,15,16,14,266,268,267,269,265,264,184,183,185,182,181,180,478,477,479,474,475,476,497,496,492,493,494,495,285,284,286,287,283,282,289,288,290,291,292,293,466,465,467,462,463,464,471,470,472,473,468,469,487,486,488,489,490,491,543,548,510,529,534,524,515,537,552,581,566,586,561,576,592,571,114,115,117,118,116,113,93,92,94,91,89,90,178,179,177,176,174,175,109,108,107,112,110,111,235,236,234,238,239,237,53,55,54,57,58,56,87,86,88,84,85,83,246,248,247,250,251,249,194,193,192,195,196,197,383,382,378,379,380,381,395,394,390,391,392,393,358,357,359,354,355,356,316,315,317,312,313,314,371,370,366,367,368,369,376,375,377,372,373,374,385,384,386,387,388,389,541,547,511,528,533,521,516,539,554,580,565,585,560,575,593,570,153,154,150,151,152,155,138,137,139,142,140,141,104,106,105,101,102,103,160,159,161,157,158,156,215,214,213,211,210,212,97,96,95,98,99,100,132,131,133,135,136,134,259,258,260,263,261,262,208,207,209,206,204,205,346,345,347,342,343,344,456,461,457,458,459,460,440,439,441,442,443,438,361,360,362,363,364,365,348,353,349,350,351,352,339,338,340,341,336,337,452,451,453,454,455,450,542,545,513,526,530,523,518,536,550,578,562,582,557,572,590,568,38,39,35,36,37,40,145,144,146,149,147,148,82,81,80,79,77,78,33,32,34,30,31,29,220,219,221,218,216,217,73,72,71,74,75,76,1,2,0,3,143,4,254,253,252,255,256,257,189,191,190,187,188,186,436,435,437,432,433,434,294,299,295,296,297,298,445,444,446,447,448,449,331,330,332,333,334,335,420,425,421,422,423,424,429,428,430,431,426,427,302,301,303,304,305,300,544,549,514,525,532,522,519,535,551,577,563,583,558,573,589,567 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#fd7de578af0812c41995e8ffd4ad83dcb5427b7eb760f7a58401ca67989e247a, 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 03:12:31 · history