Equation 677 Database

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Magma ffb6fd1865a8…

magma ffb6fd1865a8
Size
595
Isomorphism class hash
ffb6fd1865a8a53878f86bb0c7045768373470e4bb3b56b4c843c7623bf12843
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
2026-10-07 01:51:57
Display reorder
277,278,276,280,281,279,271,272,270,274,275,273,338,337,339,340,341,336,507,506,508,509,505,504,343,342,344,345,346,347,555,556,562,594,593,113,115,114,118,116,117,90,89,91,94,92,93,266,265,264,267,268,269,227,226,225,223,224,222,111,110,112,107,108,109,137,139,138,142,140,141,25,179,24,26,27,28,101,103,102,106,104,105,128,130,129,126,127,125,463,462,464,465,466,467,403,402,404,405,406,407,287,286,283,282,284,285,425,424,420,421,422,423,499,498,500,501,502,503,456,461,457,458,459,460,401,400,396,397,398,399,551,510,546,526,531,521,536,542,519,588,583,574,559,563,579,569,206,204,205,208,209,207,161,163,162,165,166,164,250,249,251,248,246,247,234,236,235,239,237,238,180,182,181,185,183,184,85,84,83,87,88,86,59,61,60,63,64,62,202,201,200,199,203,198,69,68,70,67,65,66,390,395,391,392,393,394,491,490,486,487,488,489,364,363,365,360,361,362,453,452,454,455,450,451,370,369,371,366,367,368,388,387,389,384,385,386,496,495,497,492,493,494,554,513,549,529,534,524,539,544,516,592,587,577,560,567,582,572,196,195,197,192,193,194,43,42,41,44,45,46,260,259,258,261,262,263,211,212,210,215,213,214,144,143,145,146,147,148,119,121,120,124,122,123,12,14,13,16,17,15,153,152,154,149,150,151,21,23,22,19,20,18,437,436,432,433,434,435,315,314,316,317,312,313,305,304,300,301,302,303,468,473,469,470,471,472,298,297,299,294,295,296,429,428,430,431,426,427,320,319,321,322,323,318,553,512,548,528,533,523,538,543,515,591,586,576,561,566,581,571,4,3,5,1,0,2,49,48,47,50,51,52,242,240,241,243,244,245,218,217,216,220,221,219,6,8,7,11,9,10,53,55,54,58,56,57,75,74,76,73,71,72,190,189,191,186,187,188,79,78,77,80,81,82,351,350,352,353,348,349,327,326,328,329,324,325,375,374,376,377,372,373,292,291,293,288,289,290,381,380,382,383,378,379,359,358,354,355,356,357,332,331,333,334,335,330,552,511,547,527,532,522,537,541,517,590,585,575,557,565,580,570,178,177,176,173,175,174,133,132,131,134,135,136,257,256,255,252,253,254,230,229,228,232,233,231,37,36,35,39,40,38,98,100,99,97,95,96,158,160,159,156,157,155,33,32,34,29,30,31,169,167,168,170,171,172,419,418,414,415,416,417,441,440,442,443,438,439,480,485,481,482,483,484,306,311,307,308,309,310,475,474,476,477,478,479,411,410,412,413,408,409,446,445,447,448,449,444,550,514,545,525,530,520,535,540,518,589,584,573,558,564,578,568 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {12, 30} (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 2026-10-07 01:51:58 · history