Equation 677 Database

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Magma 1d88b958038a…

magma 1d88b958038a
Size
399
Isomorphism class hash
1d88b958038a5ce7220fa1d349bfde783fe5e0980b97eda7df34d1eadddcd738
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 15:43:00
Display reorder
273,274,275,276,277,278,270,271,272,282,283,284,285,286,287,279,280,281,381,327,320,304,201,328,202,321,305,329,203,322,297,330,204,323,298,331,205,315,299,316,332,206,300,324,198,317,301,325,199,318,302,326,200,319,303,210,336,313,288,211,337,314,289,212,338,306,290,213,339,307,291,214,340,308,292,215,341,309,293,207,333,310,294,208,334,311,295,209,335,312,296,391,385,386,392,92,177,233,188,93,180,178,225,94,181,179,226,95,182,171,227,96,183,172,228,173,97,184,229,98,185,174,230,90,186,175,231,91,187,176,232,197,101,170,217,189,102,162,218,190,103,163,219,191,104,164,220,192,105,165,221,193,106,166,222,194,107,167,223,195,99,168,224,196,100,169,216,383,389,390,384,248,29,78,125,249,117,30,79,250,118,31,80,251,119,32,72,243,120,33,73,34,244,121,74,245,122,35,75,246,123,27,76,247,124,28,77,109,241,22,87,110,242,23,88,111,234,24,89,112,235,25,81,113,236,26,82,114,237,18,83,115,238,19,84,116,239,20,85,108,240,21,86,388,398,397,387,348,157,342,15,350,16,158,344,352,17,159,346,354,9,160,349,356,10,161,351,153,358,11,353,343,12,154,355,345,13,155,357,347,14,156,359,8,367,150,361,1,369,151,363,0,371,152,364,2,373,144,366,3,375,145,368,4,377,146,370,5,360,147,372,6,362,148,374,7,365,149,376,394,395,396,393,68,266,140,52,69,53,267,141,70,45,268,142,71,46,269,143,63,47,261,135,262,64,48,136,65,49,263,137,66,50,264,138,67,51,265,139,36,61,259,133,37,62,260,134,38,54,252,126,39,55,253,127,40,56,254,128,41,57,255,129,42,58,256,130,43,59,257,131,44,60,258,132,379,378,380,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#c2d30d5cdb435ade9b4740933d825814f2ef3d5c827614563e8d8e2a30971153, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 15:43:01 · history