Equation 677 Database

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Magma 8e6f9110a5a4…

magma 8e6f9110a5a4
Size
321
Isomorphism class hash
8e6f9110a5a47afa74a39043ed99fc78c2b781afcbd4fa58e0c00dc3b3b6e9be
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 22:49:38
Display reorder
311,247,245,240,275,50,57,34,223,49,56,33,222,58,47,35,220,59,48,36,221,248,244,241,274,43,38,55,216,44,39,53,217,42,37,54,215,41,46,52,219,242,243,246,273,40,45,51,218,106,107,108,109,110,111,112,113,288,286,287,285,304,309,300,315,282,280,294,283,84,91,205,99,85,92,206,100,93,82,209,98,94,83,207,96,95,81,208,97,77,211,90,104,279,295,281,284,76,210,89,105,214,80,86,103,212,78,87,101,213,79,88,102,161,162,160,164,165,163,167,168,169,170,171,166,310,302,305,316,199,194,175,29,195,198,174,30,269,271,265,238,197,193,173,31,270,268,264,239,196,192,172,32,187,180,204,27,188,178,202,28,189,179,203,26,266,267,272,237,177,190,201,24,176,191,200,25,123,124,122,126,127,125,128,129,291,292,293,290,303,319,301,312,276,277,278,289,65,17,69,114,64,16,68,115,234,251,252,255,19,67,71,116,18,66,70,117,63,73,21,118,250,253,235,256,62,72,20,119,74,60,22,120,75,61,23,121,254,249,236,257,4,5,3,1,0,2,185,186,183,181,182,184,308,306,307,318,144,139,11,153,137,145,12,154,138,146,10,155,147,135,14,152,148,136,15,150,149,134,13,151,259,233,260,262,258,232,261,263,130,9,143,159,6,133,140,158,7,131,141,156,8,132,142,157,224,225,226,227,228,229,230,231,298,296,297,299,314,317,313,320 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, 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 22:49:39 · history