Equation 677 Database

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Magma 13783b821d4a…

magma 13783b821d4a
Size
396
Isomorphism class hash
13783b821d4a743f5be7cbc5447d7343e87b9f7f991bdcbfe414aaa735d856e7
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 10:59:51
Display reorder
376,360,317,353,337,263,318,265,211,264,66,267,212,266,67,273,213,272,58,279,214,278,59,350,338,348,314,351,203,249,60,256,204,250,61,257,205,251,62,258,206,252,63,259,207,253,64,260,208,349,315,352,336,316,254,261,209,65,255,262,210,168,160,161,162,163,164,165,166,167,326,159,327,328,329,363,392,383,381,379,344,39,53,188,236,40,54,189,237,29,55,190,227,30,56,182,228,31,57,183,229,32,15,364,367,310,16,184,230,33,17,185,231,34,307,332,342,356,306,333,343,35,269,271,232,36,275,277,233,311,357,365,37,234,51,186,38,235,52,187,143,149,136,137,138,139,140,141,142,144,145,146,147,148,322,390,375,385,380,373,359,358,121,281,101,93,122,282,102,80,108,283,103,81,109,280,104,82,110,287,105,83,111,288,106,84,112,290,107,85,113,292,94,86,114,294,95,87,115,296,96,88,116,298,97,89,117,300,98,90,118,99,302,91,119,100,304,92,120,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,382,395,394,377,362,308,347,1,150,22,247,2,270,23,248,3,276,24,238,4,323,309,368,5,151,25,239,6,152,26,240,7,153,27,241,8,154,28,242,9,324,354,345,10,155,18,243,11,156,19,244,12,157,20,245,13,21,158,246,14,355,325,346,0,198,202,191,192,193,194,195,196,197,199,200,201,334,335,366,393,389,386,387,371,321,339,179,50,130,218,180,268,131,219,181,274,132,220,169,42,133,221,170,43,134,222,171,44,135,223,172,45,123,224,173,46,124,340,330,312,361,341,331,313,125,225,174,47,126,226,175,48,127,215,176,128,49,216,177,129,41,217,178,75,79,68,69,70,71,72,73,74,76,77,78,319,320,372,384,388,378,391 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#6b9c8d3036868a08370ad1878f562fe0c41374f2f554fb65dddd9aba27979bde, 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 10:59:53 · history