Equation 677 Database

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Magma 02e0c245e313…

magma 02e0c245e313
Size
595
Isomorphism class hash
02e0c245e313914a30e9cf42ad79bf6b61c2d5573d6bc4fc2b8047a03e61d9e9
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 00:37:59
Display reorder
4,3,5,1,0,2,395,394,396,392,393,391,355,354,353,352,350,351,365,367,366,364,362,363,360,359,361,358,356,357,521,514,512,511,559,240,245,241,242,243,244,191,190,187,188,189,186,23,22,18,19,20,21,202,201,203,198,199,200,212,211,213,214,215,210,254,253,255,256,257,252,174,179,175,176,177,178,87,86,88,89,84,85,73,72,74,75,76,77,224,223,225,226,227,222,313,347,314,315,316,317,330,329,328,327,348,326,373,375,374,378,376,377,408,406,407,410,411,409,483,482,507,506,480,481,343,472,434,471,433,470,531,528,520,519,510,518,569,572,564,586,566,550,551,545,574,583,192,197,193,194,195,196,17,16,13,14,15,12,37,36,38,39,40,41,7,6,8,9,10,11,278,277,279,280,281,276,46,45,47,42,43,44,154,153,155,150,151,152,248,247,249,250,251,246,173,172,168,169,170,171,303,302,304,305,300,301,450,449,418,491,499,490,488,500,489,475,476,474,509,493,501,492,451,452,477,440,439,448,437,438,379,381,380,384,382,383,325,467,429,466,428,465,540,523,535,542,541,534,544,590,562,582,576,563,584,581,594,567,275,274,270,271,272,273,287,286,283,284,285,282,158,157,159,160,161,156,108,113,109,110,111,112,133,132,134,135,136,137,70,69,71,66,67,68,107,106,102,103,104,105,205,204,206,207,208,209,295,294,296,297,298,299,162,167,163,164,165,166,334,336,335,331,332,333,388,390,389,385,386,387,342,349,341,339,340,338,402,401,403,398,399,400,460,479,504,397,505,478,487,405,486,508,485,404,536,537,515,524,513,522,552,557,568,577,591,593,571,578,570,589,267,266,268,269,264,265,96,101,98,99,100,97,54,59,55,56,57,58,142,141,143,138,139,140,119,118,114,115,116,117,52,51,53,48,49,50,292,291,293,288,289,290,82,81,83,78,79,80,148,147,149,144,145,146,131,130,126,127,128,129,473,435,436,345,346,344,416,415,417,412,414,413,369,368,370,371,372,441,432,469,337,468,431,430,311,310,312,307,308,309,422,420,502,498,503,421,533,526,530,529,527,543,560,553,592,547,558,561,549,548,556,588,229,228,230,231,232,233,124,123,120,121,122,125,220,219,221,216,217,218,184,183,185,180,181,182,60,65,61,62,63,64,91,90,92,93,94,95,236,235,237,238,239,234,27,26,28,29,24,25,262,261,263,258,259,260,30,35,31,32,33,34,495,456,455,454,453,494,461,424,423,306,425,484,445,447,446,444,442,443,458,496,419,497,457,459,320,319,318,322,323,321,324,464,427,462,426,463,538,539,516,532,517,525,565,579,580,554,555,587,585,573,546,575 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = the submagma generated by {54, 66} (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 00:38:01 · history