Equation 677 Database

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Magma f1a85eac421a…

magma f1a85eac421a
Size
321
Isomorphism class hash
f1a85eac421ae756d71f6fd5741b55d1493e41a5f9caab11ebd25118919c064d
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 22:59:36
Display reorder
300,93,138,52,120,20,94,139,18,53,119,95,140,19,51,182,178,141,22,209,223,96,142,21,49,245,242,229,206,50,118,91,136,15,57,115,92,137,16,58,113,56,90,135,17,114,88,183,175,54,117,218,228,38,55,116,89,246,239,210,222,315,305,310,307,279,278,277,276,199,283,282,200,281,280,287,286,201,285,284,291,290,198,288,289,295,294,196,293,292,299,298,197,297,296,271,270,190,269,268,275,274,191,273,272,264,267,266,192,265,255,254,193,252,253,259,258,194,256,257,263,262,195,261,260,319,320,317,318,157,147,125,13,204,230,248,237,126,14,158,148,33,127,205,231,149,8,128,12,186,185,9,129,10,159,150,7,130,11,155,145,36,123,61,156,146,37,124,62,122,154,184,174,60,151,143,35,224,211,152,144,34,121,59,153,247,238,225,212,308,316,312,313,66,44,170,102,24,64,45,25,168,103,65,46,23,169,104,69,47,27,171,101,67,48,28,172,179,68,176,26,188,100,189,42,30,233,97,234,43,207,166,219,167,173,41,29,98,63,39,32,249,220,240,208,236,232,243,213,40,31,165,99,309,306,303,301,4,187,177,70,180,5,160,181,86,71,3,161,112,87,72,1,162,111,85,73,0,163,109,83,74,2,164,110,84,75,202,132,105,79,76,203,131,106,80,77,81,235,226,107,214,6,134,221,216,241,251,227,244,217,215,250,133,108,82,78,311,304,314,302 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#e0ddb86ffdf58ba66baf4adb67528755a1dfe5eefeff33f7cfcb062fa9d34ece, 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 22:59:37 · history