Equation 677 Database

← all  ·  ← by size  ·  ← size 396

Magma 90c22fab4156…

magma 90c22fab4156
Size
396
Isomorphism class hash
90c22fab41565da15a9a53747d0de4bab2fa776141dd064dad753ad2eec6eb0f
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
2026-10-02 06:08:22
Display reorder
379,367,327,325,312,42,346,119,115,43,249,120,116,44,250,121,117,45,279,122,278,46,251,328,326,313,347,329,118,47,242,123,108,48,243,124,109,37,244,125,110,38,245,126,111,246,39,127,112,345,311,330,324,331,40,247,113,128,41,248,114,217,209,210,211,212,213,214,215,216,338,218,339,340,337,362,380,383,386,392,308,87,222,266,267,15,88,223,268,16,89,224,269,17,90,225,270,18,91,226,271,19,92,364,368,309,93,227,272,20,94,228,273,12,320,341,351,354,321,342,352,21,95,229,13,274,96,230,275,353,356,363,85,264,22,220,86,265,14,221,25,31,32,33,34,35,36,23,24,26,27,28,29,30,310,381,378,384,389,373,360,361,169,170,281,193,201,171,282,194,202,172,283,181,203,173,280,182,204,174,287,183,205,175,288,184,206,176,290,185,207,177,292,186,208,178,294,187,195,179,296,188,196,298,180,189,197,300,166,190,198,191,167,302,199,192,168,304,200,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,385,394,395,382,358,344,319,150,151,104,238,72,152,105,239,277,153,106,240,73,332,323,366,74,142,107,241,75,143,97,231,76,144,98,232,77,145,99,233,78,333,357,343,79,146,100,234,80,101,147,235,81,102,148,236,82,237,149,103,83,365,334,322,84,55,59,60,49,50,51,52,53,54,56,57,58,314,315,355,376,387,390,393,372,348,318,160,161,139,255,71,154,140,256,276,219,141,257,61,162,129,258,62,163,130,259,63,164,131,260,64,165,132,261,65,155,133,349,316,335,359,350,317,336,134,262,66,135,156,263,67,136,157,252,68,253,158,137,69,254,159,138,70,1,11,2,3,4,5,6,7,8,9,10,0,306,307,371,391,375,388,377 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#9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699, 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 2026-10-02 06:08:24 · history