Equation 677 Database

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Magma d79822d59f7f…

magma d79822d59f7f
Size
595
Isomorphism class hash
d79822d59f7faab2acbbfc5f5efc4cc6bba80292d7d000d40eb2cd5ef19064cd
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
2026-10-06 19:14:16
Display reorder
27,26,28,29,24,25,291,290,292,293,288,289,406,405,407,404,403,402,389,390,391,392,393,394,412,411,413,409,408,410,526,529,522,560,591,235,234,237,238,239,236,191,190,186,187,188,189,113,112,108,109,110,111,214,213,215,210,211,212,265,264,266,267,268,269,302,301,303,304,305,300,72,77,73,74,75,76,151,150,152,153,154,155,78,83,79,80,81,82,91,90,92,93,94,95,374,373,375,371,372,370,339,341,340,343,344,342,380,379,381,378,376,377,414,415,416,419,417,418,475,474,509,508,473,472,318,462,425,464,426,463,530,524,514,512,516,527,570,585,573,593,548,565,578,554,551,557,7,6,9,10,11,8,70,69,71,66,67,68,193,192,194,195,196,197,84,89,85,86,87,88,20,19,21,22,23,18,262,261,263,258,259,260,122,121,123,124,125,120,208,207,209,204,205,206,149,148,144,145,146,147,37,36,38,39,40,41,458,459,401,491,499,492,496,501,497,494,495,493,504,460,500,461,424,423,490,457,456,454,455,453,359,358,357,362,360,361,363,482,436,480,435,481,534,541,540,510,515,539,547,550,552,584,583,572,556,563,564,571,45,44,47,42,43,46,15,14,16,17,12,13,117,116,118,119,114,115,100,99,101,96,97,98,52,51,53,48,49,50,246,251,247,248,249,250,107,106,102,103,104,105,244,243,245,240,241,242,253,252,254,255,256,257,203,202,198,199,200,201,321,323,322,324,325,326,330,332,331,328,329,327,349,348,347,350,351,352,314,313,312,315,316,317,471,470,507,353,506,469,466,320,467,505,465,319,535,536,520,513,521,519,543,549,555,582,580,581,545,579,590,558,278,277,280,281,276,279,62,61,63,64,65,60,1,5,0,2,3,4,169,168,170,171,172,173,56,55,57,58,59,54,227,226,222,223,224,225,143,142,138,139,140,141,136,135,137,132,133,134,284,283,285,286,287,282,130,129,131,126,127,128,468,428,427,345,346,356,398,400,399,395,397,396,368,367,366,364,365,437,446,486,382,487,447,448,388,387,386,385,384,383,422,420,502,498,503,421,531,523,525,542,517,532,559,546,567,576,574,562,587,561,588,553,296,295,298,299,294,297,219,218,220,221,216,217,175,174,176,177,178,179,228,233,229,230,231,232,34,33,35,30,31,32,157,156,158,159,160,161,273,272,274,275,270,271,183,182,184,185,180,181,162,167,163,164,165,166,306,311,307,308,309,310,489,452,451,449,450,488,479,434,433,355,432,478,444,443,445,442,440,441,429,476,354,477,430,431,337,336,338,334,335,333,369,485,439,483,438,484,538,537,518,511,533,528,575,544,577,566,586,569,592,594,589,568 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = the submagma generated by {18, 48} (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 2026-10-06 19:14:17 · history