Equation 677 Database

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Magma 855187d23712…

magma 855187d23712
Size
321
Isomorphism class hash
855187d23712cef41d9afb49ca5f93407140556e44196f42ace6b17cdb14d349
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 22:20:56
Display reorder
300,66,119,192,90,206,64,120,190,91,207,65,191,89,205,121,118,62,195,86,202,116,63,193,87,203,117,61,194,88,204,57,125,187,81,197,55,126,188,82,198,56,127,189,80,196,84,124,60,186,200,122,58,184,85,201,123,59,185,83,199,309,301,305,307,295,6,292,294,293,299,4,296,298,297,291,288,290,289,5,2,279,276,278,277,3,283,280,282,281,0,287,284,286,285,259,12,257,258,256,263,10,261,262,260,255,11,253,254,252,270,8,271,269,268,9,275,273,274,272,7,267,264,266,265,317,318,320,319,170,103,29,247,244,171,101,30,251,248,169,28,243,241,102,99,166,25,159,73,100,167,26,234,232,98,168,27,239,236,161,94,20,16,71,162,92,21,17,72,160,93,19,18,70,15,97,164,23,67,95,165,24,13,68,96,163,22,14,69,313,316,302,306,179,37,136,230,216,180,38,134,231,214,178,135,229,215,39,40,182,139,226,219,41,183,137,227,217,42,181,138,228,218,177,35,131,221,211,175,36,132,222,212,176,34,133,220,213,224,31,173,130,210,32,174,128,225,208,33,172,129,223,209,310,312,311,304,245,43,108,146,246,249,44,109,147,250,240,107,148,242,45,46,1,104,149,152,47,233,105,150,235,48,237,106,151,238,74,49,114,144,155,75,50,115,145,153,76,51,113,143,154,140,52,77,110,158,53,78,111,141,156,54,79,112,142,157,315,303,308,314 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#055eb219830141adc126b0e3c095dec26895b5c9338d223a671ccb522fe00e95, 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 22:20:57 · history