Equation 677 Database

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Magma 3931e309052e…

magma 3931e309052e
Size
381
Isomorphism class hash
3931e309052e63a046b1b82dd4529fbc4931cf4c3d8fa6e50341433560813ea1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:27:44
Display reorder
380,182,177,187,192,197,202,132,135,125,292,147,142,257,262,252,242,247,237,112,117,120,11,6,286,96,100,105,85,281,90,157,162,152,172,297,167,316,317,315,313,314,312,3,2,275,71,76,81,227,222,232,207,212,217,55,61,66,17,16,270,30,40,36,51,46,265,372,346,362,356,369,332,335,351,340,377,183,178,188,193,198,203,133,138,128,293,148,143,258,263,253,243,248,238,113,118,123,21,20,288,98,103,108,88,283,93,158,163,153,173,298,168,302,301,300,305,303,304,19,18,278,73,78,83,228,223,233,208,213,218,58,63,68,23,22,273,33,42,38,53,48,268,373,348,363,357,367,333,338,353,343,378,180,175,185,191,196,201,130,137,126,290,146,141,255,260,250,241,246,236,110,115,122,12,13,287,97,101,107,86,280,91,155,160,151,171,295,166,308,306,307,311,309,310,5,4,276,70,75,80,226,221,230,205,210,215,56,60,65,14,15,271,32,44,35,50,45,266,370,345,360,355,365,330,336,350,341,376,184,179,189,194,199,204,134,139,129,294,149,144,259,264,254,244,249,239,114,119,124,29,28,289,99,104,109,89,284,94,159,164,154,174,299,169,329,327,328,326,324,325,27,26,279,74,79,84,229,224,234,209,214,219,59,64,69,25,24,274,34,43,39,54,49,269,374,349,364,359,368,334,339,354,344,379,181,176,186,190,195,200,131,136,127,291,145,140,256,261,251,240,245,235,111,116,121,9,10,285,95,102,106,87,282,92,156,161,150,170,296,165,319,320,318,322,323,321,8,7,277,72,77,82,225,220,231,206,211,216,57,62,67,0,1,272,31,41,37,52,47,267,371,347,361,358,366,331,337,352,342,375 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {67} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:27:45 · history