Equation 677 Database

← all  ·  ← by size  ·  ← size 396

Magma 1cac033daced…

magma 1cac033daced
Size
396
Isomorphism class hash
1cac033dacedb334563c483272365fa8f25c89899049f11f80cc94d293dbf16e
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 05:46:22
Display reorder
378,358,324,314,320,132,325,265,62,267,122,268,63,270,123,276,64,274,124,199,65,125,114,317,321,326,322,316,66,126,115,54,67,127,116,55,68,128,117,53,69,129,118,51,70,130,119,52,59,327,323,315,319,328,120,50,60,121,131,49,61,0,2,3,4,5,6,7,8,9,306,1,307,308,309,354,386,383,385,391,351,204,240,269,271,205,241,275,277,206,230,133,213,207,231,134,214,208,232,135,215,209,233,359,363,343,234,136,216,210,235,137,217,211,346,329,344,362,347,318,345,200,236,57,218,201,237,58,219,342,365,355,212,202,238,56,203,263,239,266,182,174,175,176,177,178,179,180,181,183,184,185,186,173,339,376,375,381,393,373,357,356,109,281,98,78,110,282,85,79,111,283,86,80,112,280,87,81,113,287,88,82,99,288,89,83,100,290,90,84,101,292,91,71,102,294,92,72,103,296,93,73,104,298,94,74,105,300,95,75,106,302,96,76,107,97,304,77,108,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,379,394,395,377,360,353,335,36,142,273,154,22,143,279,155,23,144,254,156,24,331,350,361,25,145,255,157,26,146,256,158,27,147,257,159,28,148,258,160,29,332,367,333,30,138,259,150,31,139,260,151,32,140,261,152,33,141,262,153,34,368,330,334,35,253,245,246,247,248,249,250,251,252,242,243,244,348,349,366,382,387,390,389,372,352,338,20,188,272,172,10,187,278,161,149,198,220,162,21,189,221,163,11,190,222,164,12,191,223,165,13,192,224,166,14,193,225,336,310,340,364,337,311,341,226,167,15,194,227,168,16,195,228,169,17,196,229,170,18,264,197,171,19,37,40,41,42,43,44,45,46,47,48,38,39,312,313,371,392,380,388,384 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#7638a5f4265b8c038acb6c1c40b431ab2d5856fd12b04f7ad747e562d533a407, 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 05:46:25 · history