Equation 677 Database

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Magma 0da2cd35067b…

magma 0da2cd35067b
Size
595
Isomorphism class hash
0da2cd35067b09cec4354abfef2e9cdb850637f80974cb61c29a40d96fba9d10
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 23:04:09
Display reorder
25,24,26,27,28,29,39,38,40,41,36,37,150,149,151,152,153,154,352,351,353,348,349,350,311,310,309,307,308,306,515,511,555,560,586,266,267,163,264,265,212,201,147,143,144,145,146,56,55,51,52,53,54,50,49,47,233,232,48,243,242,191,192,76,77,170,169,171,172,173,273,219,278,216,277,217,218,244,194,246,195,245,193,178,9,10,11,7,8,420,419,421,424,422,423,486,488,487,491,489,490,438,437,439,440,441,442,394,393,392,389,390,391,409,408,407,412,410,411,448,447,446,445,443,444,506,507,501,509,502,508,520,524,522,531,543,546,523,557,553,591,563,589,566,593,547,584,141,137,142,139,140,138,135,134,136,131,132,133,32,31,33,34,35,30,93,92,94,95,96,91,126,125,127,128,129,130,114,118,115,116,117,251,253,148,254,255,202,203,272,270,168,271,252,213,200,105,106,107,103,104,499,498,500,503,504,505,430,429,428,426,427,425,464,466,465,463,461,462,318,320,319,322,323,321,363,365,364,360,361,362,493,492,494,496,497,495,289,290,288,292,293,291,545,544,518,514,512,517,513,570,571,578,580,582,583,585,575,581,67,69,68,65,66,70,62,61,57,58,59,60,97,102,98,99,100,101,110,109,111,112,113,108,79,78,80,81,82,83,74,73,75,72,71,280,284,90,286,282,247,248,281,285,175,287,283,279,226,17,13,14,15,16,335,334,333,330,331,332,406,405,404,402,403,401,347,346,345,343,344,342,301,300,302,305,303,304,453,452,454,450,451,449,314,313,312,317,315,316,299,298,297,294,295,296,533,532,526,510,519,525,516,573,576,562,565,561,594,569,554,558,124,120,119,122,123,121,155,258,204,256,205,257,183,186,234,184,235,185,231,182,181,44,45,46,166,165,167,164,268,269,12,223,224,179,180,225,197,249,198,250,199,196,262,211,261,210,263,209,190,241,238,64,239,240,325,324,326,329,327,328,457,456,455,459,460,458,435,434,436,431,432,433,341,340,339,336,337,338,384,383,385,387,388,386,482,481,480,485,483,484,472,471,470,467,468,469,538,537,536,535,539,540,534,556,564,577,590,579,588,574,568,572,19,21,20,23,18,22,43,229,230,42,227,228,177,176,222,221,6,220,260,207,208,160,161,162,158,157,159,156,206,259,237,236,188,189,187,63,89,88,84,85,86,87,4,0,3,1,2,5,174,215,276,275,274,214,414,413,415,418,416,417,354,356,355,359,357,358,371,370,369,367,368,366,374,373,372,375,376,377,397,396,395,400,398,399,477,479,478,474,475,476,473,378,379,382,380,381,542,541,528,529,530,521,527,550,549,559,587,552,548,567,592,551 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = the submagma generated by {6, 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 23:04:10 · history