Equation 677 Database

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Magma e0954d15c6c9…

magma e0954d15c6c9
Size
381
Isomorphism class hash
e0954d15c6c9205175e77aa42af338008612d5c6d43b8976286488a827f58eda
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:31:38
Display reorder
380,261,71,191,307,72,79,64,225,86,156,241,165,67,201,309,74,81,60,235,88,246,170,68,206,310,75,82,61,210,89,69,175,251,181,311,76,83,62,215,84,266,271,276,281,286,160,291,66,196,308,73,80,65,230,87,151,70,256,186,306,77,78,63,220,85,297,364,340,341,339,343,366,342,359,379,371,260,100,190,328,107,108,93,226,115,155,240,166,96,200,324,103,110,95,236,117,245,171,97,205,325,104,111,90,211,118,98,176,250,180,326,105,112,91,216,119,265,270,275,280,287,161,290,101,195,329,102,109,94,231,116,150,99,255,185,327,106,113,92,221,114,295,361,345,346,344,348,367,347,356,377,370,262,59,192,312,31,38,52,227,45,157,242,167,55,202,314,33,40,48,237,47,247,172,56,207,315,34,41,49,212,42,57,177,252,182,316,35,36,50,217,43,268,273,278,283,288,162,292,54,197,313,32,39,53,232,46,152,58,257,187,317,30,37,51,222,44,298,362,338,334,337,336,365,335,357,375,372,263,14,193,323,21,28,7,228,1,158,243,168,16,203,319,23,24,9,238,2,248,173,17,208,320,18,25,10,213,3,12,178,253,183,321,19,26,11,218,4,267,272,277,282,285,163,293,15,198,318,22,29,8,233,0,153,13,258,188,322,20,27,6,223,5,296,363,330,354,331,332,368,333,358,376,373,264,130,194,305,137,138,123,229,145,159,244,169,126,204,300,133,140,125,239,147,249,174,127,209,302,134,141,120,214,148,128,179,254,184,303,135,142,121,219,149,269,274,279,284,289,164,294,131,199,301,132,139,124,234,146,154,129,259,189,304,136,143,122,224,144,299,360,350,351,349,353,369,352,355,378,374 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#7d1ca7f19a6476d5d19958a01b2b150bc7a0c60d280d02593b805c82a69bb42e, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:31:39 · history