Equation 677 Database

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Magma 70566e1e9f8d…

magma 70566e1e9f8d
Size
595
Isomorphism class hash
70566e1e9f8d1406094c8719456aea505251f391e1712e73c85a6042d4cf9446
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 19:35:00
Display reorder
69,68,70,71,66,67,43,42,44,45,46,47,426,428,427,431,429,430,362,361,360,364,365,363,327,329,328,326,324,325,510,526,525,555,552,268,269,168,270,271,213,189,102,103,104,100,101,13,12,14,15,16,11,73,72,74,219,220,75,218,217,174,175,35,34,152,156,153,154,155,243,205,247,204,248,202,203,214,170,215,172,216,171,173,1,2,3,4,0,345,347,346,342,343,344,301,300,302,303,304,305,476,474,475,478,479,477,411,413,412,409,410,408,295,294,296,298,299,297,442,441,443,440,438,439,503,502,501,498,500,499,527,547,516,513,534,514,532,559,558,587,589,548,572,576,556,554,8,10,9,6,7,5,112,111,113,114,115,116,84,89,85,86,87,88,126,125,127,128,123,124,59,58,54,55,56,57,147,146,148,149,150,241,262,162,260,261,209,210,257,256,161,258,259,208,184,94,90,91,92,93,397,396,398,400,401,399,403,402,404,405,406,407,387,389,388,386,384,385,468,470,469,472,473,471,509,508,507,506,504,505,319,318,320,323,321,322,381,383,382,380,378,379,519,521,531,533,515,528,546,582,557,585,560,566,574,569,568,567,143,145,144,141,142,140,40,39,41,36,37,38,27,26,28,23,24,25,130,129,131,132,133,134,20,19,21,22,17,18,30,33,31,32,29,274,280,169,281,277,272,273,275,279,151,278,276,242,231,99,95,96,97,98,467,466,465,464,462,463,313,312,314,315,316,317,293,292,291,289,290,288,285,287,286,282,284,283,340,339,341,337,338,336,369,371,370,367,368,366,444,446,445,449,447,448,537,539,535,512,511,536,517,579,575,551,594,549,550,571,586,584,50,52,51,48,49,53,160,255,206,253,207,254,197,196,239,198,240,199,221,177,176,76,77,78,165,164,166,163,267,263,167,266,264,211,212,265,185,230,186,229,187,188,232,192,233,190,234,191,183,225,226,83,227,228,416,415,414,419,417,418,485,484,483,480,481,482,424,423,425,420,421,422,390,392,391,394,395,393,435,437,436,432,433,434,308,307,306,309,310,311,494,493,492,496,497,495,541,545,522,524,523,518,520,562,592,593,570,583,591,565,578,561,60,62,61,64,65,63,159,251,252,158,249,250,194,193,235,236,135,237,222,179,178,79,80,81,137,136,138,139,195,238,224,223,180,181,182,82,110,109,105,106,107,108,122,121,117,118,119,120,157,201,245,246,244,200,377,376,375,374,372,373,330,332,331,335,333,334,355,354,356,357,358,359,461,460,459,456,457,458,489,491,490,487,486,488,452,451,450,453,454,455,348,350,349,353,351,352,530,529,543,540,542,538,544,563,581,564,573,580,590,588,577,553 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 {6, 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 2026-10-07 19:35:01 · history