Equation 677 Database

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Magma 655bf7f58802…

magma 655bf7f58802
Size
321
Isomorphism class hash
655bf7f58802d37ac5d958b1c34cdf5d73bf9f678c90f50347057dad550924ed
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 22:41:26
Display reorder
300,68,9,244,184,16,245,10,185,17,66,243,11,67,183,15,8,240,71,180,12,6,241,69,181,13,7,242,70,182,14,1,63,190,250,22,64,0,191,251,23,2,65,189,249,21,62,3,186,246,18,60,4,187,247,19,61,5,188,248,20,308,301,315,313,269,40,268,271,270,273,41,275,274,272,264,39,265,266,267,36,253,252,255,254,37,257,256,259,258,38,261,260,262,263,46,292,295,293,294,296,47,298,297,299,45,289,290,288,291,277,42,279,276,278,280,43,283,281,282,284,44,287,285,286,318,319,320,317,86,110,72,165,172,73,108,166,173,84,74,109,85,167,171,113,75,89,164,168,111,76,87,162,169,112,77,88,163,170,116,92,156,78,178,90,114,157,79,179,115,91,158,80,177,95,119,159,81,174,93,117,160,82,175,94,118,161,83,176,316,305,302,312,232,131,225,100,212,226,129,101,210,233,227,130,231,99,211,127,224,228,96,215,128,222,229,97,213,126,223,230,98,214,122,238,106,216,207,239,120,107,217,208,121,237,105,218,209,234,125,102,219,206,235,123,103,220,204,236,124,104,221,205,303,310,309,311,142,30,200,148,56,198,31,149,54,143,199,32,141,147,55,33,203,138,144,59,34,201,139,145,57,35,202,140,146,58,28,133,154,195,51,134,29,155,196,52,27,132,153,197,53,136,24,150,194,50,137,25,151,192,48,135,26,152,193,49,304,307,306,314 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#8513f42721191fc76047535e55730c0acbdcae75cecf1dd6e4636ed6d0c5727e, 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 22:41:27 · history