Equation 677 Database

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Magma 29755a98732c…

magma 29755a98732c
Size
595
Isomorphism class hash
29755a98732c87c7f456e2020d6975027f86a78acbaef78d2c7c281bd50a71fb
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 06:10:01
Display reorder
85,84,86,89,87,88,52,51,53,49,50,48,105,107,106,104,102,103,279,278,280,281,282,277,391,396,392,393,394,395,527,523,516,563,556,95,94,90,91,92,93,6,8,7,10,11,9,173,172,171,176,174,175,167,166,165,162,163,164,191,187,195,183,256,253,222,221,220,223,224,225,249,245,244,246,247,248,148,147,149,145,146,144,433,437,434,435,436,276,413,412,414,409,410,411,302,301,303,304,305,306,386,385,387,388,389,390,299,298,300,295,296,297,469,468,470,471,472,473,360,359,355,356,357,358,406,405,407,408,403,404,510,534,552,524,537,538,543,547,574,583,593,573,569,554,568,555,209,208,213,211,212,210,239,238,240,243,241,242,250,254,180,189,193,185,1,2,0,4,5,3,79,78,80,83,81,82,56,55,54,57,58,59,109,108,110,112,113,111,226,228,227,229,230,231,397,402,398,399,400,401,449,448,444,445,446,447,464,463,465,466,467,462,504,509,505,506,507,508,353,352,354,349,350,351,424,423,425,426,421,422,258,259,260,261,262,263,312,311,307,308,309,310,551,548,528,545,518,540,522,517,588,579,575,577,591,584,582,580,37,36,41,39,40,38,160,159,161,158,156,157,131,130,129,128,126,127,44,43,42,45,46,47,61,60,62,65,63,64,73,72,74,77,75,76,27,29,28,24,25,26,32,31,30,35,33,34,374,373,375,376,377,378,499,498,500,501,502,503,461,460,456,457,458,459,315,314,316,317,318,313,491,490,486,487,488,489,331,336,332,333,334,335,442,441,443,438,439,440,292,291,293,294,289,290,536,514,512,515,525,531,519,521,594,572,587,564,565,581,590,571,201,200,196,197,198,199,215,214,216,219,217,218,252,257,181,190,194,186,116,115,114,117,118,119,139,138,140,143,141,142,13,12,14,17,15,16,100,99,101,97,98,96,169,168,170,177,178,179,455,454,450,451,452,453,329,328,330,325,326,327,342,341,337,338,339,340,428,427,429,430,431,432,476,475,477,478,479,474,287,286,288,283,284,285,322,321,323,324,319,320,370,369,371,372,367,368,546,539,526,544,529,541,533,511,592,559,567,576,557,566,561,558,155,154,150,151,152,153,18,20,19,22,23,21,134,133,132,137,135,136,66,68,67,70,71,69,188,184,192,182,255,251,232,234,233,236,237,235,204,203,202,207,205,206,120,122,121,123,124,125,418,417,419,420,415,416,496,495,497,492,493,494,484,483,485,480,481,482,267,266,268,269,264,265,348,347,343,344,345,346,273,272,274,275,270,271,380,379,381,382,383,384,365,364,366,361,362,363,513,530,549,535,520,532,542,550,553,560,585,570,562,578,589,586 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#ca4e87f44b5aa8ee937e3111d7e18929d38c701d18b6266af0f19751e7c29bcd, 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 2026-10-08 06:10:08 · history