Equation 677 Database

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Magma f90d94328ee8…

magma f90d94328ee8
Size
321
Isomorphism class hash
f90d94328ee8aa08a31fd8669a44546b0b3678d6fe76ed2ba6db01889a65e309
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 22:50:56
Display reorder
300,11,10,12,9,7,8,16,17,18,15,13,14,83,59,70,94,60,95,84,71,58,96,82,72,55,93,79,69,56,91,80,67,57,92,81,68,76,65,100,89,77,66,101,90,78,64,102,88,61,75,99,85,62,73,97,86,63,74,98,87,301,302,304,303,32,31,33,34,35,36,37,38,39,40,41,42,266,264,267,265,268,269,270,271,272,273,274,275,260,261,262,263,252,253,254,255,256,257,258,259,291,288,289,290,295,292,293,294,299,296,297,298,285,287,284,286,277,279,276,278,281,283,280,282,320,318,317,319,53,52,54,51,49,50,43,44,45,46,47,48,182,180,183,181,188,189,190,191,196,197,198,199,173,172,174,175,157,156,158,159,165,164,166,167,231,228,229,230,239,236,237,238,247,245,244,246,221,223,220,222,204,207,205,206,213,215,212,214,312,309,310,311,105,104,106,107,1,103,3,0,2,6,4,5,123,121,122,120,124,125,127,126,128,129,131,130,116,117,119,118,108,109,111,110,112,113,115,114,146,145,144,147,150,148,149,151,154,152,153,155,140,142,141,143,133,134,132,135,136,138,137,139,305,308,307,306,26,25,27,28,29,30,23,24,22,19,20,21,184,185,186,187,193,195,192,194,200,203,201,202,176,179,177,178,161,163,160,162,168,171,169,170,234,233,235,232,242,240,243,241,250,248,251,249,224,226,227,225,209,210,211,208,216,218,219,217,316,315,314,313 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, 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 22:50:57 · history