Equation 677 Database

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Magma f093edd028c2…

magma f093edd028c2
Size
381
Isomorphism class hash
f093edd028c242e4ced5d6bd0238e0efb398b6689247c542ceca246f610afa87
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 23:39:35
Display reorder
380,259,279,269,249,229,239,209,219,199,149,189,148,141,142,140,299,144,143,132,133,134,135,136,294,284,131,130,128,129,127,2,3,137,1,0,18,289,169,174,163,154,159,264,274,254,234,244,224,301,300,302,303,304,305,194,214,204,184,138,139,5,147,4,179,145,146,334,369,358,364,379,344,354,339,349,374,256,275,266,245,225,235,206,216,196,20,185,19,30,29,79,296,27,28,63,64,65,66,67,290,280,62,61,59,60,58,32,33,31,35,36,34,285,165,170,160,151,157,260,270,250,232,241,220,323,321,322,320,318,319,191,211,200,180,56,96,80,82,81,175,83,84,330,366,356,361,375,340,350,335,345,370,258,278,268,248,228,238,208,218,198,126,188,125,118,119,117,298,121,120,24,22,23,26,25,293,283,37,38,39,40,41,14,13,114,17,15,16,288,168,173,164,153,158,263,273,253,233,243,223,317,315,316,314,312,313,193,213,203,183,115,116,12,124,11,178,122,123,333,368,357,363,378,343,353,338,348,373,255,276,265,246,227,237,205,215,195,87,186,86,76,74,75,295,77,78,49,47,48,68,10,291,281,46,45,43,44,42,53,54,55,50,51,52,286,166,171,162,150,156,262,272,252,230,242,222,324,325,326,327,328,329,190,212,202,181,21,57,7,85,6,176,9,8,332,365,355,362,376,341,351,336,346,371,257,277,267,247,226,236,207,217,197,107,187,108,100,101,99,297,98,97,88,89,90,91,92,292,282,111,112,110,113,109,73,71,72,70,69,93,287,167,172,161,152,155,261,271,251,231,240,221,310,311,309,307,308,306,192,210,201,182,95,94,106,103,102,177,104,105,331,367,359,360,377,342,352,337,347,372 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {70} 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 23:39:36 · history