Equation 677 Database

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Magma 2e65f5590006…

magma 2e65f5590006
Size
321
Isomorphism class hash
2e65f5590006e71ede8b05f941c9b1b3156ddd76dd401c3141ced06f3b5f0662
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 22:21:15
Display reorder
300,199,245,80,138,209,200,243,78,139,207,198,79,140,208,244,241,202,83,141,205,242,203,81,142,206,240,201,82,143,204,197,251,136,75,215,195,249,137,76,213,77,196,250,135,214,247,193,132,74,211,248,194,133,72,212,246,192,134,73,210,302,308,313,315,273,272,32,275,274,265,264,30,266,267,269,31,270,271,268,257,256,35,259,258,261,260,33,262,263,253,252,34,254,255,297,296,299,27,298,288,289,290,28,291,29,292,293,295,294,281,280,282,26,283,284,285,286,24,287,277,276,278,25,279,319,318,317,320,85,149,8,185,99,86,147,6,183,100,84,7,184,101,148,145,88,11,181,98,146,89,9,182,96,144,87,10,180,97,91,155,191,3,105,92,153,189,4,106,5,90,154,190,107,151,94,187,2,104,152,95,188,1,102,150,93,186,0,103,307,316,312,305,233,223,14,127,113,231,224,12,128,111,232,13,126,112,222,226,229,17,130,109,227,230,15,131,110,225,228,16,129,108,239,221,125,20,119,237,219,123,18,117,19,238,220,124,118,217,235,121,23,115,218,236,122,21,116,216,234,120,22,114,310,303,311,304,55,173,43,163,65,56,171,44,164,63,54,42,162,64,172,169,58,46,166,61,170,59,47,167,62,168,57,45,165,60,53,179,161,41,71,51,177,159,39,69,40,52,178,160,70,175,49,157,37,67,176,50,158,38,68,174,48,156,36,66,309,301,314,306 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#0afaa5a95ac3a042540e79b2adb5184e36490c06a1d05440665a030a584e7e24, 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 22:21:15 · history