Equation 677 Database

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Magma 9528f91236bc…

magma 9528f91236bc
Size
321
Isomorphism class hash
9528f91236bcfbe09d00035a845fda438274488ced9f3d7e8e7de31493e75c6b
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 22:49:42
Display reorder
300,136,232,200,26,182,202,137,24,180,233,198,231,135,25,181,228,193,132,29,185,229,195,133,27,183,230,196,134,28,184,238,213,32,142,188,239,215,30,143,186,237,211,31,141,187,205,234,35,138,191,207,235,33,139,189,209,236,34,140,190,306,308,313,315,270,268,269,249,271,273,274,250,275,272,264,265,266,251,267,253,252,254,248,255,257,256,258,246,259,261,260,262,247,263,293,292,240,294,295,297,296,241,298,299,288,289,242,290,291,276,277,243,278,279,280,281,244,282,283,284,285,245,286,287,320,318,317,319,112,40,56,71,11,54,113,69,9,41,55,39,111,70,10,36,59,108,67,7,37,57,109,68,8,38,58,110,66,6,46,51,62,118,2,47,52,60,119,1,45,53,61,117,0,50,42,65,114,5,48,43,63,115,3,49,44,64,116,4,302,316,312,304,75,93,100,147,220,101,76,148,221,94,99,95,77,149,219,92,96,74,146,216,90,97,72,144,217,91,98,73,145,218,84,106,153,81,226,85,107,154,82,227,86,105,155,83,225,102,87,152,80,222,103,88,150,78,223,104,89,151,79,224,310,305,311,301,160,201,13,121,174,14,161,122,175,203,12,199,159,120,176,192,16,156,124,177,194,17,157,125,178,197,15,158,123,179,212,19,127,166,172,214,20,128,167,173,210,18,126,165,171,22,204,130,162,168,23,206,131,163,169,21,208,129,164,170,307,303,314,309 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#b0c577ef9e4c05d7925e972279aa7c10376825c460b06aa55c85bf856c0bbca9, 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 22:49:43 · history