Equation 677 Database

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Magma bfcec58a4de2…

magma bfcec58a4de2
Size
595
Isomorphism class hash
bfcec58a4de2a334b9193dfc07d71a230d100299f1590e977305c88b08d63122
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 13:20:49
Display reorder
279,281,280,278,277,276,270,271,272,275,273,274,509,508,505,504,506,507,282,283,284,285,286,287,295,294,296,297,298,299,555,556,594,592,593,267,269,268,264,265,266,178,177,179,176,174,175,20,19,18,22,23,21,223,222,224,226,227,225,228,230,229,233,231,232,15,17,16,14,12,13,108,110,109,111,112,113,105,107,106,103,104,102,114,116,115,118,119,117,413,412,408,409,410,411,452,451,453,454,455,450,420,425,421,422,423,424,405,404,406,407,402,403,417,416,418,419,414,415,492,497,493,494,495,496,301,300,302,303,304,305,551,536,521,548,516,511,541,526,533,563,577,573,557,582,587,569,262,261,263,259,260,258,170,169,168,171,172,173,6,8,7,11,9,10,220,219,221,217,218,216,210,212,211,215,213,214,125,124,123,120,122,121,99,101,100,96,97,98,94,93,95,92,90,91,144,146,145,148,149,147,400,399,401,396,397,398,444,445,446,447,448,449,382,381,383,378,379,380,392,391,393,394,395,390,389,388,384,385,386,387,489,488,490,491,486,487,291,290,292,293,288,289,550,535,520,547,519,510,540,525,532,562,578,572,560,584,589,567,244,243,245,240,242,241,155,154,153,151,150,152,141,143,142,140,139,138,203,202,201,200,198,199,192,194,193,197,195,196,49,48,50,51,52,53,76,75,77,73,74,72,34,33,35,32,30,31,68,67,66,69,70,71,358,357,359,354,355,356,463,462,464,465,466,467,352,351,353,348,349,350,306,311,307,308,309,310,343,342,344,345,346,347,485,484,480,481,482,483,318,323,319,320,321,322,553,538,523,549,518,513,543,529,534,565,580,575,559,585,588,570,246,248,247,249,250,251,157,156,158,161,159,160,129,131,130,128,126,127,235,234,236,238,239,237,190,189,191,186,187,188,133,132,134,135,136,137,1,2,0,3,4,5,54,56,55,58,59,57,65,64,63,60,61,62,427,426,428,429,430,431,469,468,470,471,472,473,333,332,334,335,330,331,324,329,325,326,327,328,340,339,341,336,337,338,498,503,499,500,501,502,432,437,433,434,435,436,554,539,524,545,517,514,544,528,530,566,581,576,558,586,591,571,255,257,256,252,253,254,163,162,164,167,165,166,47,46,45,43,44,42,185,184,183,182,181,180,205,204,206,207,208,209,36,38,37,41,39,40,28,27,29,25,26,24,87,89,88,85,86,84,80,79,78,81,82,83,440,439,441,442,443,438,461,460,456,457,458,459,360,365,361,362,363,364,372,377,373,374,375,376,367,366,368,369,370,371,476,474,477,478,479,475,316,315,317,312,313,314,552,537,522,546,515,512,542,527,531,564,579,574,561,583,590,568 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = the submagma generated by {30, 60} (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 13:20:51 · history