Equation 677 Database

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Magma 13f61603d829…

magma 13f61603d829
Size
321
Isomorphism class hash
13f61603d829f6edf8948b389ffa5ca67833c2859939fc3b56ce53cd5d59e93a
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 22:28:15
Display reorder
300,62,124,42,145,133,63,122,40,146,134,64,123,41,144,135,120,65,44,141,132,43,66,121,142,130,119,228,226,143,131,60,115,37,137,125,61,113,38,138,126,59,114,39,136,127,118,56,36,139,128,116,57,34,140,129,117,58,35,232,231,306,302,310,314,295,294,246,292,293,298,299,247,296,297,290,291,248,289,288,278,279,249,276,277,250,283,282,280,281,286,287,251,284,285,259,258,244,257,256,262,263,245,261,260,255,254,243,253,252,270,271,240,269,268,274,275,241,273,272,267,266,242,264,265,318,317,320,319,179,201,72,166,225,235,202,70,167,33,178,200,71,168,24,197,175,68,165,25,69,176,198,163,26,199,177,67,164,27,170,192,78,158,28,171,193,76,159,29,169,191,77,160,30,195,173,74,161,31,196,174,75,162,32,194,172,73,234,224,303,301,313,309,189,212,17,88,156,190,213,15,89,157,188,211,16,87,155,208,185,13,84,152,14,186,209,85,153,210,187,12,86,154,181,204,23,80,148,182,205,21,81,149,180,203,22,79,147,206,184,19,83,233,207,236,20,229,151,237,183,18,82,150,304,307,316,312,100,111,9,219,46,98,112,10,217,47,99,110,11,218,45,107,96,8,215,49,6,97,108,216,50,109,95,7,214,48,92,102,1,223,52,90,103,0,221,53,91,101,2,222,51,105,94,3,239,55,106,230,4,238,227,104,93,5,220,54,311,315,305,308 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#3f4c16e16e9bd422beeb4e3c1331ed0b07b0ac931af0d47b2d7497fadfe20a6b, 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 22:28:15 · history