Equation 677 Database

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Magma 1797618a632c…

magma 1797618a632c
Size
396
Isomorphism class hash
1797618a632c127f862466816739ca097e7a35c59e853b4c507da96773cd0f03
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-05 11:07:24
Display reorder
376,368,313,329,321,81,347,40,127,82,248,41,128,83,249,42,129,73,279,43,277,74,250,314,330,318,348,315,119,75,241,44,120,242,76,45,121,46,77,243,122,47,78,244,123,48,79,245,124,319,316,346,328,320,38,246,125,80,39,247,126,216,208,209,210,211,212,213,214,215,338,217,339,340,337,364,378,382,386,392,324,266,221,151,152,97,267,222,141,98,268,223,142,99,269,224,143,100,270,225,144,101,271,366,359,325,272,226,145,102,273,227,103,146,350,341,351,360,326,342,352,147,104,228,274,148,105,229,278,353,358,365,149,264,95,219,150,265,96,220,2,3,4,5,6,7,8,9,10,11,12,13,14,15,306,375,379,381,391,373,362,363,168,169,281,192,200,170,282,193,201,171,283,180,202,172,280,181,203,173,287,182,204,174,288,183,205,175,290,184,206,292,176,185,207,186,177,294,194,187,178,296,195,188,179,298,196,165,189,300,197,166,190,302,198,167,191,304,199,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,385,394,395,380,354,345,327,69,70,31,237,115,71,32,238,276,72,33,239,116,317,311,367,117,61,34,240,118,62,35,230,106,63,36,231,107,37,64,232,108,343,356,312,109,233,65,27,110,234,66,28,111,67,235,29,112,68,236,30,113,357,344,310,114,164,156,157,158,159,160,161,162,163,153,154,155,335,336,361,383,387,390,393,372,334,307,57,58,254,136,16,1,255,137,275,218,256,138,17,59,257,139,18,60,258,140,19,49,259,130,20,50,260,131,21,261,51,331,308,332,355,349,309,333,52,262,22,132,53,263,23,54,133,251,24,55,134,252,25,56,135,253,26,0,93,94,84,85,86,87,88,89,90,91,92,322,323,371,389,377,388,384 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#8622272f99ed7258e0e5c3e0e3c3c55307035c123d24328e2a163f5e0fb74bfb, M = {75} 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, 79): MacNeish's product over GF(79); 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 2026-10-05 11:07:25 · history