Equation 677 Database

← all  ·  ← by size  ·  ← size 396

Magma e5ddc19cd1c6…

magma e5ddc19cd1c6
Size
396
Isomorphism class hash
e5ddc19cd1c6af517760c8f892cfbf1aeab6c16e0721cc27b7be43d01b136e02
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 05:41:31
Display reorder
394,367,330,350,318,64,331,28,47,65,161,29,48,66,162,30,49,67,163,31,50,68,164,311,319,321,332,312,51,57,165,32,52,58,166,33,53,59,167,34,54,60,168,25,55,61,169,26,56,320,333,310,317,334,62,27,45,46,63,170,24,35,38,39,40,41,42,43,44,36,313,37,314,315,316,354,385,390,384,388,325,4,246,239,91,5,247,240,92,6,248,241,82,7,249,242,83,8,250,243,84,9,251,363,355,307,252,233,85,10,253,234,86,11,344,342,351,366,345,343,324,1,254,235,87,0,255,236,88,306,364,362,2,89,244,237,238,90,3,245,98,104,105,106,93,94,95,96,97,99,100,101,102,103,326,379,382,393,387,373,356,357,111,281,131,136,112,282,132,137,113,283,133,138,114,280,134,139,115,287,135,140,116,288,122,141,117,290,123,142,118,292,124,143,119,294,125,144,120,296,126,145,121,298,127,146,107,300,128,147,108,129,302,148,109,110,304,130,149,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,375,377,381,359,329,347,219,200,150,266,220,201,151,267,221,202,152,256,222,339,327,365,223,203,153,257,224,204,154,258,225,205,155,259,226,206,156,260,227,353,368,346,228,196,157,261,229,197,158,262,230,198,159,263,231,160,199,264,232,361,338,328,265,218,210,211,212,213,214,215,216,217,207,208,209,340,341,360,383,380,391,386,372,335,352,73,268,182,184,74,269,183,185,75,270,171,186,76,271,172,187,77,272,173,188,78,273,174,189,79,274,175,190,80,275,176,336,322,348,358,337,323,349,177,191,81,276,178,192,69,277,179,193,70,180,278,194,71,72,279,181,195,12,17,18,19,20,21,22,23,13,14,15,16,308,309,371,376,389,378,392 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#49bc88ab7a8d9583ec223800dafe9d1a5b1436a8177256550637a54e04ef8e30, 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 05:41:33 · history