Equation 677 Database

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Magma 4c96c5dd6a3a…

magma 4c96c5dd6a3a
Size
321
Isomorphism class hash
4c96c5dd6a3a312c899033a6736aec01244c270c30b88251e700b4df8a795c49
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:22:01
Display reorder
300,133,46,145,162,163,134,47,146,160,164,135,48,147,161,165,49,136,144,232,233,50,137,143,159,248,240,228,230,158,166,51,138,150,155,167,52,139,151,153,168,53,140,152,154,169,141,54,149,157,170,229,208,148,156,171,142,241,247,231,234,304,305,315,306,285,180,284,287,286,277,178,276,279,278,281,179,280,283,282,183,297,296,299,298,181,289,288,291,290,182,293,292,295,294,175,264,265,267,266,176,268,269,271,270,177,272,273,275,274,260,174,261,263,262,252,172,253,255,254,256,173,257,259,258,318,317,319,320,103,10,79,89,225,218,236,245,87,120,102,9,78,88,224,204,106,82,92,123,7,104,80,90,121,8,105,81,91,122,12,6,75,84,117,13,4,76,85,118,14,5,77,86,119,1,11,74,214,223,3,0,73,83,116,2,237,244,213,222,308,312,310,307,190,29,20,60,66,188,30,18,58,64,189,31,19,59,65,32,193,16,56,69,33,191,17,57,67,34,192,15,55,68,28,185,24,210,71,207,186,206,62,211,27,187,23,63,70,184,25,22,209,243,235,238,205,242,212,249,26,21,61,72,303,302,316,301,98,35,112,199,129,96,36,110,197,127,97,37,111,198,128,38,101,115,195,132,39,99,113,196,130,40,100,114,194,131,41,94,108,203,125,42,95,109,201,126,43,217,221,202,227,93,44,220,251,226,215,239,219,250,246,216,45,107,200,124,314,313,309,311 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#19ea6a1480a1f5a2ac1b5eeb32448a05ed8c6404ec648162b4da66f77bce13ec, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); 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 2026-10-01 22:22:02 · history