Equation 677 Database

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Magma d51e3258ebc2…

magma d51e3258ebc2
Size
381
Isomorphism class hash
d51e3258ebc20231876908b78eb7dbac09612b7c593c4b6ae0fbd675d09b4e49
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 23:47:09
Display reorder
380,78,83,298,99,89,304,305,301,300,302,158,148,153,143,132,93,303,137,48,223,43,33,38,28,165,173,160,183,188,178,53,58,293,62,68,73,233,238,243,247,253,258,104,109,113,118,123,128,198,203,193,213,218,208,0,228,1,3,4,2,273,268,263,283,288,278,348,358,353,338,372,333,343,363,368,378,77,80,297,97,87,316,317,312,313,314,157,147,152,142,134,91,315,139,47,222,42,32,37,27,169,172,164,182,187,177,52,57,292,60,67,72,232,237,242,249,252,257,103,107,112,117,121,127,197,202,192,212,217,207,19,227,18,16,17,15,272,267,262,282,287,277,347,357,352,337,371,332,342,362,367,377,75,82,296,98,88,325,326,327,328,329,156,145,150,140,130,92,324,135,46,220,41,30,35,26,168,171,163,180,186,175,50,55,291,64,66,70,230,236,241,246,251,255,102,105,110,115,120,125,195,200,190,211,216,206,6,226,5,8,7,14,270,265,261,280,285,276,346,356,351,335,370,331,341,361,366,375,76,81,295,96,85,321,322,320,318,319,155,146,151,141,133,90,323,138,45,221,40,31,36,25,167,170,162,181,185,176,51,56,290,61,65,71,231,235,240,245,250,256,100,108,111,116,122,126,196,201,191,210,215,205,13,225,12,10,11,9,271,266,260,281,286,275,345,355,350,336,373,330,340,360,365,376,79,84,299,95,86,309,310,308,306,307,159,149,154,144,131,94,311,136,49,224,44,34,39,29,166,174,161,184,189,179,54,59,294,63,69,74,234,239,244,248,254,259,101,106,114,119,124,129,199,204,194,214,219,209,24,229,23,21,22,20,274,269,264,284,289,279,349,359,354,339,374,334,344,364,369,379 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, 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 23:47:10 · history