Equation 677 Database

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Magma f9a635a413c9…

magma f9a635a413c9
Size
595
Isomorphism class hash
f9a635a413c9ef1cb06d20f6bd0769e70c9524d07464725e420705a0a43593dc
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 20:29:22
Display reorder
411,413,412,415,416,414,329,328,327,324,325,326,346,345,344,343,341,342,382,381,383,386,384,385,364,363,365,368,366,367,537,534,517,515,538,505,484,453,503,504,454,483,455,393,451,449,450,434,433,432,430,431,429,320,322,321,491,463,323,490,489,317,462,318,319,396,398,397,394,395,472,79,78,80,81,82,83,209,208,204,205,206,207,23,22,18,19,20,21,85,84,86,87,88,89,143,142,138,139,140,141,126,131,127,128,129,130,280,279,281,276,277,278,269,268,264,265,266,267,25,24,26,27,28,29,43,42,44,45,46,47,533,518,530,531,513,511,569,553,580,549,561,551,550,558,556,590,452,444,448,446,447,445,358,357,359,361,362,360,349,348,347,351,352,350,374,373,372,369,370,371,311,313,312,314,315,316,308,307,306,310,309,488,35,34,30,31,32,33,157,156,158,159,160,161,217,216,218,219,220,221,234,239,235,236,237,238,163,162,164,165,166,167,169,168,170,171,172,173,202,201,203,198,199,200,133,132,134,135,136,137,213,212,214,215,210,211,66,71,67,68,69,70,522,523,529,532,512,528,572,555,570,582,571,581,577,586,584,579,339,338,337,335,336,340,388,387,389,391,392,390,422,421,420,418,419,417,380,379,378,375,376,377,423,425,424,426,427,428,334,333,332,331,330,509,155,154,150,151,152,153,77,76,72,73,74,75,149,148,144,145,146,147,54,59,55,56,57,58,291,290,292,293,288,289,226,225,227,222,223,224,39,38,40,41,36,37,90,95,91,92,93,94,196,195,197,192,193,194,60,65,61,62,63,64,544,540,519,514,520,521,583,562,565,563,592,578,564,566,567,552,437,436,438,439,440,435,403,476,477,498,404,497,470,469,471,466,467,468,502,482,481,442,443,441,457,456,458,459,506,485,460,508,507,461,486,487,117,116,118,119,114,115,182,181,183,184,185,180,178,177,179,174,175,176,299,298,294,295,296,297,252,257,253,254,255,256,52,51,53,48,49,50,282,287,283,284,285,286,97,96,98,99,100,101,188,187,189,190,191,186,243,242,244,245,240,241,543,539,525,526,527,524,554,587,575,574,589,576,573,557,560,591,300,302,304,305,303,301,399,492,473,400,493,494,410,480,501,479,409,500,499,408,478,405,406,407,356,355,354,353,464,465,495,496,474,475,401,402,231,230,232,233,228,229,273,272,274,275,270,271,263,262,258,259,260,261,124,123,125,120,121,122,112,111,113,108,109,110,105,104,106,107,102,103,7,6,8,9,10,11,0,1,2,3,4,5,250,249,251,246,247,248,16,15,17,12,13,14,516,510,535,536,542,541,559,548,546,593,594,588,545,568,585,547 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#141a5ad98d093a51cbcd8d0e5f762ac857a7d54b6447f4e2b6939d4d1af2e3e9, M = the submagma generated by {12, 18} (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 20:29:23 · history