Equation 677 Database

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Magma 730c4e855b09…

magma 730c4e855b09
Size
595
Isomorphism class hash
730c4e855b09f54788cf700d4b1e2c600c28a9b638c31aaeed76eb0981793d7b
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 06:33:30
Display reorder
3,5,4,0,2,1,16,15,17,12,13,14,342,341,343,346,344,345,422,424,423,419,420,421,292,291,293,288,289,290,534,517,510,556,552,269,268,168,270,271,213,210,166,162,163,164,165,106,111,107,108,109,110,56,55,57,223,224,58,215,216,170,171,29,30,19,22,20,21,18,214,204,259,205,260,206,207,218,173,219,174,217,172,175,41,37,38,39,40,365,367,366,368,369,370,485,484,483,481,480,482,331,330,329,333,334,332,428,430,429,425,426,427,501,503,502,500,498,499,465,464,463,461,462,467,454,453,452,450,451,449,540,546,525,514,533,513,532,591,571,550,558,588,553,554,551,593,36,35,31,32,33,34,116,115,117,118,113,114,8,7,9,10,11,6,59,64,60,61,62,63,136,135,137,132,133,134,94,93,95,96,97,231,239,131,237,238,189,190,234,233,112,235,236,188,187,105,101,102,103,104,393,392,394,390,391,389,477,479,478,474,476,475,407,409,408,412,410,411,353,355,354,356,357,358,439,438,437,441,442,440,381,380,382,377,378,379,504,509,506,507,505,508,526,539,512,515,528,516,547,573,549,578,560,576,569,584,572,563,89,88,90,91,92,87,124,123,119,120,121,122,46,45,47,48,43,44,84,83,85,80,81,82,70,69,65,66,67,68,77,76,78,79,75,274,280,169,281,277,272,273,275,279,161,278,276,264,242,138,139,140,141,142,304,466,303,302,300,301,456,455,457,460,458,459,447,446,448,443,444,445,348,347,349,351,352,350,490,489,491,486,487,488,364,363,362,360,361,359,310,309,308,306,307,305,535,542,523,524,521,520,522,574,555,561,565,594,562,548,590,567,127,126,128,129,130,125,86,227,180,228,179,226,183,182,229,184,230,181,247,195,196,147,145,146,150,149,151,152,253,252,167,266,267,211,212,265,193,241,194,240,191,192,256,203,257,201,258,202,197,248,249,148,250,251,434,436,435,431,432,433,317,319,318,321,322,320,287,286,285,282,284,283,468,470,469,471,472,473,295,294,296,297,298,299,418,417,416,414,415,413,401,403,402,406,404,405,541,545,518,531,527,529,511,564,566,583,581,579,592,582,586,575,27,26,28,23,24,25,143,246,243,144,244,245,177,176,222,220,42,221,232,185,186,100,98,99,73,72,74,71,178,225,255,254,198,199,200,153,158,157,159,154,155,156,52,51,53,54,49,50,160,209,261,262,263,208,316,315,314,313,311,312,328,327,326,323,324,325,385,384,383,387,388,386,396,395,397,399,400,398,492,497,493,496,494,495,340,339,338,336,337,335,375,374,376,371,372,373,530,543,536,519,538,537,544,580,559,568,570,587,585,589,557,577 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = the submagma generated by {6, 12} (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 06:33:32 · history