Equation 677 Database

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Magma 5d6f05c862dd…

magma 5d6f05c862dd
Size
595
Isomorphism class hash
5d6f05c862ddfadc49b91b0ee9867d4e62426f59caaf443a43bc8ecce67cf131
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 03:21:49
Display reorder
334,333,335,330,331,332,438,437,439,440,441,436,414,413,415,416,417,412,465,464,460,461,462,463,271,272,270,275,273,274,555,594,588,586,587,342,344,343,346,347,345,336,341,337,338,339,340,432,431,433,434,435,430,384,383,385,386,387,388,418,423,419,420,421,422,471,470,466,467,468,469,429,428,424,425,426,427,123,125,124,120,121,122,126,128,127,131,129,130,207,209,208,206,205,204,234,235,236,239,237,238,103,102,104,105,106,107,35,34,33,32,30,31,144,146,145,149,147,148,155,154,153,150,151,152,268,267,269,264,265,266,524,529,537,549,534,511,552,544,519,569,593,580,560,575,565,585,357,353,358,355,356,354,502,507,503,504,505,506,455,454,456,457,458,459,282,287,283,284,285,286,409,509,410,411,407,408,308,307,309,310,311,306,368,367,369,370,365,366,113,112,111,110,108,109,41,40,39,37,38,36,194,192,193,196,197,195,228,230,229,232,233,231,61,60,62,63,64,65,17,16,15,14,12,13,172,171,173,168,169,170,51,53,52,49,50,48,262,261,263,258,259,260,520,525,535,545,531,512,550,540,515,566,590,577,557,571,564,582,453,449,448,451,452,450,501,500,496,497,498,499,508,348,352,349,350,351,390,389,391,392,393,394,376,375,371,372,373,374,404,403,405,406,401,402,277,281,276,278,279,280,137,136,135,134,132,133,165,167,166,164,162,163,56,55,54,58,59,57,211,212,210,214,215,213,47,46,45,43,44,42,28,27,29,25,26,24,94,93,95,90,91,92,185,184,183,180,181,182,249,251,250,248,246,247,522,527,539,546,532,514,553,541,516,570,591,578,556,573,563,584,379,381,380,377,378,382,298,297,299,294,295,296,313,312,314,315,316,317,293,292,288,289,290,291,486,485,487,488,489,484,398,397,399,400,395,396,476,475,477,472,473,474,188,187,186,191,189,190,114,116,115,119,117,118,200,198,199,202,203,201,224,223,222,225,226,227,97,96,98,99,100,101,10,9,11,7,8,6,0,1,2,3,4,5,142,141,143,140,138,139,244,243,245,241,240,242,521,526,536,547,530,513,554,542,518,567,589,576,559,572,562,581,493,495,494,491,492,490,322,321,323,318,319,320,445,444,446,447,442,443,360,359,361,362,363,364,329,328,324,325,326,327,480,479,481,482,483,478,304,303,305,300,301,302,78,80,79,81,82,83,87,89,88,86,84,85,71,70,69,67,68,66,221,220,219,216,217,218,179,178,177,175,176,174,19,18,20,22,23,21,73,72,74,75,76,77,158,157,156,159,160,161,255,257,256,254,252,253,523,528,538,548,533,510,551,543,517,568,592,579,558,574,561,583 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = the submagma generated by {30, 36} (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 03:21:51 · history