Equation 677 Database

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Magma af1165408127…

magma af1165408127
Size
381
Isomorphism class hash
af1165408127e1330659da359b9265bc1f20241348e830f748637cad9a27b590
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 23:28:00
Display reorder
380,178,188,183,203,193,198,40,46,35,273,31,28,118,288,123,103,106,111,218,208,213,233,223,228,163,153,158,173,168,298,302,301,300,305,303,304,278,58,53,68,73,63,268,3,8,11,17,23,128,293,133,138,143,148,95,90,281,78,86,81,243,237,245,254,259,264,362,348,338,343,373,357,333,368,353,378,177,187,182,202,192,197,44,49,39,272,34,27,115,286,120,100,109,113,217,207,212,232,222,227,162,152,157,172,167,297,307,308,306,310,311,309,277,57,52,67,72,62,266,1,6,13,19,21,126,291,131,135,142,145,97,92,282,76,87,82,242,238,248,252,257,262,361,347,336,342,372,358,332,367,351,377,176,185,180,201,191,196,42,47,38,271,32,25,116,285,121,102,108,114,215,205,210,231,221,226,160,151,155,171,166,295,313,314,312,316,317,315,275,55,51,66,71,61,265,0,5,12,15,20,127,292,132,137,140,147,99,94,284,77,89,84,240,235,247,253,258,263,360,345,335,341,371,356,331,365,352,375,179,189,184,204,194,199,41,45,36,274,30,29,119,289,124,104,105,110,219,209,214,234,224,229,164,154,159,174,169,299,323,321,322,320,318,319,279,59,54,69,74,64,269,4,9,14,18,24,129,294,134,139,144,149,96,91,280,79,85,80,244,239,249,250,256,261,363,349,339,344,374,359,334,369,354,379,175,186,181,200,190,195,43,48,37,270,33,26,117,287,122,101,107,112,216,206,211,230,220,225,161,150,156,170,165,296,328,329,327,325,326,324,276,56,50,65,70,60,267,2,7,10,16,22,125,290,130,136,141,146,98,93,283,75,88,83,241,236,246,251,255,260,364,346,337,340,370,355,330,366,350,376 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 = {71} 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 23:28:01 · history