Equation 677 Database

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Magma 09391dbc2fbd…

magma 09391dbc2fbd
Size
321
Isomorphism class hash
09391dbc2fbd90e80e6ae720d4cb24f028610dbba40ef6c71e1cca9667068801
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 22:49:10
Display reorder
300,121,209,51,131,85,122,210,49,132,86,123,211,50,130,87,208,120,47,134,84,206,118,48,135,82,119,207,46,133,83,42,200,112,129,76,40,201,113,127,77,41,202,114,128,78,203,45,115,125,79,204,43,116,126,80,205,44,117,124,81,306,311,301,304,289,291,191,288,290,293,295,192,292,294,296,299,193,297,298,287,284,190,285,286,279,277,188,276,278,280,283,189,281,282,197,255,252,253,254,198,259,256,257,258,199,263,261,260,262,267,196,264,265,266,271,194,268,269,270,275,195,272,273,274,320,317,318,319,240,243,136,6,58,245,247,137,7,59,249,251,138,8,60,238,239,139,9,61,186,24,140,10,62,25,187,141,11,63,142,183,30,4,56,143,184,31,5,57,144,185,29,3,55,182,145,26,1,52,180,146,27,0,53,181,147,28,2,54,314,313,308,310,233,107,13,214,96,234,108,14,212,94,235,106,12,213,95,110,232,16,217,99,111,230,17,215,97,231,109,15,216,98,19,105,224,220,91,20,103,225,218,92,18,104,226,219,93,101,22,227,223,90,102,23,228,221,88,100,21,229,222,89,312,303,302,305,177,241,72,158,242,178,244,70,156,246,179,248,71,157,250,237,176,75,161,236,32,174,73,159,154,175,33,74,160,155,67,34,168,164,151,68,35,169,162,152,69,36,170,163,153,37,66,171,167,150,38,64,172,165,148,39,65,173,166,149,309,316,315,307 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#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, 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 22:49:11 · history