Equation 677 Database

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Magma 6099e7af33ed…

magma 6099e7af33ed
Size
401
Isomorphism class hash
6099e7af33ed715d54bd00f655c6f941e5da341342950f22dc071cad599f7ec4
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: yes · normal: yes · rank: 161 (nullity 240) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 09:05:57
Display reorder
324,206,42,194,188,271,235,301,290,247,242,106,259,111,29,256,293,63,144,158,24,191,185,288,275,197,315,311,304,2,307,28,80,108,166,88,89,175,34,282,131,168,119,94,178,172,54,224,219,214,211,48,47,208,277,51,135,147,296,140,118,66,268,102,72,126,7,164,85,153,96,253,61,238,233,57,127,5,115,64,13,243,56,236,248,292,116,285,265,141,148,86,261,154,32,257,297,15,67,69,30,101,113,264,295,74,308,305,316,3,312,37,95,169,179,120,76,112,17,266,99,230,239,255,234,245,41,207,189,200,182,45,50,229,276,53,137,145,318,159,132,180,273,203,186,198,52,209,217,227,213,128,35,90,250,38,97,8,82,150,31,142,23,123,160,287,103,286,267,70,68,240,300,246,58,283,294,60,232,249,59,210,222,299,278,218,303,309,313,0,317,36,129,176,252,91,92,173,20,270,170,109,77,100,155,104,9,98,162,151,83,19,14,75,284,22,192,181,274,187,204,121,262,146,138,133,43,195,183,201,190,107,10,79,165,26,220,46,225,215,55,184,40,196,202,298,73,263,260,65,114,231,281,241,62,319,289,49,223,228,44,244,251,291,280,237,310,314,306,1,302,25,134,117,139,122,199,205,39,272,193,124,149,136,161,143,21,167,171,177,93,6,27,87,269,18,163,81,258,152,84,226,279,212,216,221,12,105,78,156,110,157,4,125,71,16,174,11,130,254,33,340,377,367,385,386,382,326,334,373,391,351,383,387,368,328,333,389,322,332,381,399,356,338,357,354,337,363,393,400,364,323,374,390,349,396,335,369,344,336,388,371,366,331,360,341,359,378,380,392,325,362,321,353,330,395,320,346,394,343,398,352,375,358,384,329,355,361,345,379,376,372,339,370,347,365,397,348,342,327,350 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 401 = 1 + 5*80, 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#632999fe988720d6e4b1122c58d44ae4b38c3c642c3b4fe2a9fb06707fadcca2, M = {0} 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, 80): MacNeish's product over GF(16) x GF(5); 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: 401.

last edited by qawbecrdtey at 2026-10-02 09:05:58 · history